A Study of ASP1570 Taken by Itself, or ASP1570 Taken Together With Either Pembrolizumab, Standard Therapies, or Both, in Adults With Solid Tumors

Inclusion Criteria: * Participant has locally-advanced (unresectable) or metastatic solid tumor malignancy which is confirmed by available pathology records or current biopsy. * Participant has at least 1 measurable lesion per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Monotherapy Escalation Cohorts and China-specific Safety Lead-in Cohort: a) Participant has progressed on standard therapies, is no longer eligible for standard therapies or has refused standard approved therapies (no limit to the number of prior treatment regimens). (UNIQUE to China: Certain tumor types with specific criteria may be prioritized at the sponsor's discretion). * Monotherapy Expansion Cohorts: a) Participant has MSS-CRC or NSCLC and has progressed was intolerant to at least 2 prior anti-cancer therapy regimens administered for metastatic disease. * Monotherapy Dose Optimization Cohorts: a) Participant has MSS-CRC or NSCLC and has progressed or was intolerant to at least 2 prior anti-cancer therapy regimens administered for metastatic disease. * Combination Therapy Escalation and/or Expansion Cohorts: a) For NSCLC (2L+) Combination Therapy Cohort only: * Participant has Stage IV NSCLC and has progressed on or after checkpoint inhibitors with or without platinum-based chemotherapy. * Participant is eligible to receive docetaxel. b) For MSS-CRC (3L+) Combination Therapy Cohorts only: * Participant must have progressed or was intolerant to at least 2 prior anti-cancer therapy regimens administered for metastatic disease. * Participant is eligible to receive TAS-102 and bevacizumab. * All Comers Combination with Pembrolizumab Cohorts only: * Participant who has progressed on standard therapies, are no longer eligible for standard therapies or has refused standard approved therapies. * Participant is eligible to receive pembrolizumab * For NSCLC (1L) Combination Therapy Cohorts only: * Participant has PD-L1 low (TPS = 1% to 49%) or negative (TPS \< 1%) and AGA negative Stage IV adenocarcinoma (mixed histology is not allowed). * Participant has not received prior systemic treatment for their advanced/metastatic NSCLC. * Participant who remains disease free for 12 months following the completion of neoadjuvant/adjuvant treatment is eligible. * Participant is eligible to receive pembrolizumab + pemetrexed + carboplatin. * For MSS-CRC (2L) Combination Therapy Cohorts only: * Participant is AGA negative and HER2 negative. * mFOLFOX6 + Bevacizumab: * Participant must have progressed or was intolerant to first line with irinotecan-based therapy, or previous therapy without oxaliplatin. * Participant is eligible to receive mFOLFOX6 and bevacizumab. * FOLFIRI + Bevacizumab: * Participant must have progressed or was intolerant to first line with oxaliplatin-based therapy, or previous therapy without irinotecan. * Participant is eligible to receive FOLFIRI and bevacizumab. * Eligibility of backfill participants should follow cohort specific criteria for which they are being utilized. * Participant has an Eastern Cooperative Oncology Group (ECOG) Status of 0 or 1 within 7 days before the first dose of study drug. * Participant's adverse events (excluding alopecia) from prior anti-cancer therapies have resolved or improved to grade 1 at least 14 days prior to the first dose of study intervention. Note: Participants with type 1 diabetes mellitus and endocrinopathies stably maintained on appropriate replacement therapy are allowed. * Participant has adequate organ function prior to start of study treatment (within 7 days prior to study intervention treatment initiation) as indicated by the following laboratory values. If a participant has received a recent blood transfusion, the laboratory tests must be obtained \>= 2 weeks after any blood transfusion: Absolute Neutrophil Count (ANC) \>= 1500/µL; Platelets \>= 100,000/µL; Hemoglobin \>= 9 g/dL (Criterion must be met without packed red blood cell transfusion within the 2 weeks prior. Participants can be on stable dose of erythropoietin (approximately ≥ 3 months); Creatinine clearance \>= 45 mL/min (calculated by Cockcroft-Gault equation); Total Bilirubin either (a) \<= 1.5 x ULN or (b) Direct bilirubin \<= ULN and total bilirubin \< 3 x ULN (for participants with Gilbert's syndrome); aspartate aminotransferase (AST) \[serum glutamic oxaloacetic transaminase (SGOT)\] and alanine aminotransferase (ALT) \[serum glutamic pyruvic transaminase (SGPT)\] \<= 2.5 x ULN without liver metastases (or \<= 5 x ULN if liver metastases are present); serum potassium \>= 3.4mEg/L; serum magnesium \>= 1.7mg/dL; serum ionized calcium \>= 4.7 mg/dL; Thyroid stimulating hormone (TSH) within normal limits. Note: if TSH is not within normal limits at baseline, participant may still be eligible if T3 /or FT4 is within the normal limits. * Participant has activated partial thromboplastin time and international normalized ratio (INR) \<= 1.5 x ULN and is not receiving anticoagulation. * Female participant is not pregnant confirmed by pregnancy test or confirmed to be of non-childbearing potential and at least one of the following conditions apply: * Not a woman of childbearing potential (WOCBP) * WOCBP who agrees to follow the contraceptive guidance from the time of informed consent through at least 45 days after final ASP1570 administration or at least 120 days after administration of pembrolizumab. * Females participating in the study should be advised to use a highly effective contraception method during treatment and for 2 months after the last dose of docetaxel, and for 6 months after the last dose of TAS-102 and bevacizumab. * Females participating in the study should be advised to use a highly effective contraception method during treatment and for 9 months after the last dose of mFOLFOX6. * (UNIQUE to South Korea): Females participating in the study should be advised to use a highly effective contraception method during treatment and for 15 months after the last dose of mFOLFOX6. * Females participating in the study should be advised to use a highly effective contraception method during treatment and for 6 months after the last dose of FOLFIRI. * (UNIQUE to South Korea): Females participating in the study should be advised to use a highly effective contraception method during treatment and for 7 months after the last dose of FOLFIRI. * Females participating in the study should be advised to use a highly effective contraception method during treatment and for 6 months after treatment with carboplatin, pemetrexed and pembrolizumab. * Female participant must agree not to breastfeed starting at screening and throughout the study period and for at least 45 days after final ASP1570 administration or at least 120 days after administration of pembrolizumab. * Females participating in the study should be advised to not breastfeed during and for 45 days after treatment of docetaxel. * Females participating in the study should be advised to not breastfeed during treatment and for 6 months after the last dose of TAS-102 and bevacizumab. * Females participating in the study should be advised to not breastfeed during treatment and for 45 days after the last dose of mFOLFOX6 or FOLFIRI. * Females participating in the study should be advised to not breastfeed during treatment and for 4 months after treatment with a regimen of carboplatin, pemetrexed, and pembrolizumab. * Female participant must not donate ova starting at first dose of study intervention and throughout the study period and for at least 45 days after final ASP1570 administration or at least 120 days after administration of pembrolizumab. * Females participating in the study should be advised to not donate ova during treatment and for 2 months after the last dose of docetaxel. * Females participating in the study should be advised to not donate ova during treatment and for 6 months after the last dose of TAS-102, bevacizumab or FOLFIRI. * (UNIQUE to South Korea): Females participating in the study should be advised to not donate ova during treatment and for 7 months after the last dose of FOLFIRI. * Females participating in the study should be advised to not donate ova during treatment and for 9 months after the last dose of mFOLFOX6. * (UNIQUE to South Korea): Females participating in the study should be advised to not donate ova during treatment and for 15 months after the last dose of mFOLFOX6. * Females participating in the study should be advised to not donate ova for 6 months after treatment with a regimen of carboplatin, pemetrexed and pembrolizumab. * Male participant with female partner(s) of childbearing potential (including breastfeeding partner) must agree to use contraception throughout the treatment period and for at least 45 days after final ASP1570 administration or at least 120 days after administration of pembrolizumab. * Males participating in the study should be advised to use a highly effective contraception method during treatment and for 4 months after the last dose of docetaxel. * Males participating in the study should be advised to use a highly effective contraception method during treatment and for 3 months after the last dose of TAS-102 and bevacizumab. * Males participating in the study should be advised to use a highly effective contraception method during treatment and for 6 months after the last dose of mFOLFOX6. * (UNIQUE to South Korea): Males participating in the study should be advised to use a highly effective contraception method during treatment and for 12 months after the last dose of mFOLFOX6. * Males participating in the study should be advised to use a highly effective contraception method during treatment and for 3 months after the last dose of FOLFIRI. * Males participating in the study should be advised to use a highly effective contraception method during treatment and for 6 months after the last dose of a regimen of carboplatin, pemetrexed and pembrolizumab. * Male participant must not donate sperm during the treatment period and for at least 45 days after final ASP1570 administration or at least 120 days after administration of pembrolizumab. * Males participating in the study must not donate sperm for at least 4 months after the last dose of docetaxel. * Males participating in the study must not donate sperm for at least 3 months after the last dose of TAS-102 and bevacizumab. * Males participating in the study must not donate sperm during treatment and for 6 months after the last dose of mFOLFOX6. * (UNIQUE to South Korea): Males participating in the study should be advised to not donate sperm during treatment and for 12 months after the last dose of mFOLFOX6. * Males participating in the study must not donate sperm during treatment and for 3 months after the last dose of FOLFIRI. * Males participating in the study must not donate sperm during treatment and for 6 months after the last dose of a regimen of carboplatin, pemetrexed and pembrolizumab. * Male participant with pregnant partner(s) must agree to remain abstinent or use a condom for the duration of the pregnancy throughout the study period and for at least 45 days after final ASP1570 administration or at least 120 days after administration of pembrolizumab. * Males participating in the study with pregnant partner(s) should be advised to remain abstinent or use a condom during treatment and for 4 months after the last dose of docetaxel. * Males participating in the study with pregnant partner(s) should be advised to remain abstinent or use a condom during treatment and for 6 months after the last dose of TAS-102 and bevacizumab. * Males participating in the study with pregnant partner(s) should be advised to remain abstinent or use a condom during treatment and for 6 months after the last dose of mFOLFOX6. * (UNIQUE to South Korea): Males participating in the study with pregnant partner(s) should be advised to remain abstinent or use a condom during treatment and for 12 months after the last dose of mFOLFOX6. * Males participating in the study with pregnant partner(s) should be advised to remain abstinent or use a condom during treatment and for 3 months after the last dose of FOLFIRI. * Males participating in the study with pregnant partner(s) should be advised to remain abstinent or use a condom during treatment and for 6 months after the last dose of a regimen of carboplatin, pemetrexed and pembrolizumab. * Participant agrees not to participate in another interventional study while receiving study treatment in the present study. Exclusion Criteria: * Participant has received antineoplastic therapy, including investigational therapy within 28 days or 5 half-lives (whichever is shorter) (antitumor traditional Chinese medicine within 14 days) prior to the start of study intervention administration. * Participant requires or has received systemic steroid therapy or any other immunosuppressive therapy within 14 days prior to the first dose of IP. Participants using a physiologic replacement dose of hydrocortisone or its equivalent (defined as up to 10 mg prednisone) are allowed. * Participant requires strong or moderate CYP2D6 inhibitors (e.g., bupropion, fluoxetine, paroxetine, duloxetine, abiraterone) during the study. * Participant has symptomatic central nervous system (CNS) metastases or participant has evidence of unstable CNS metastases even if asymptomatic (e.g., progression on scans). Participants with previously treated CNS metastases are eligible, if they are clinically stable and have no evidence of CNS progression by imaging for at least 4 weeks prior to start of study treatment and are on a stable dose of ≤ 10 mg/day of prednisone or equivalent for at least 2 weeks (if requiring steroid treatment). Participant does not have leptomeningeal disease. * Participant has an autoimmune disease. Participants with type 1 diabetes mellitus, endocrinopathies stably maintained on appropriate replacement therapy are allowed. * Participant was discontinued from prior immunomodulatory therapy due to a toxicity that requires permanent discontinuation per toxicity management guidelines that was mechanistically related (e.g., immune related) to the agent. * Participant has a known history of human immunodeficiency virus (HIV) infection. However, participants with HIV with cluster of differentiation 4 (CD4)+ T-cell counts ≥ 350 cells/µL and no history of AIDS-defining opportunistic infections within the past 6 months are eligible. NOTE: Screening for HIV infection should be conducted per local requirements. * Participant has any of the following per screening serology test: * Hepatitis A virus (HAV) antibodies (immunoglobulin M \[IgM\]) * Positive hepatitis B surface antigen (HBsAg). For participants with negative HBsAg, but positive HBcAB, an HBV DNA test will be performed and if positive the participants will be excluded. * Hepatitis C virus (HCV) antibodies unless HCV RNA is undetectable * Participant has received a live or live attenuated vaccine against infectious diseases within 28 days prior to the first dose of study intervention. * Participant has a history of noninfectious pneumonitis/interstitial lung disease \[ILD\], that required steroids, or currently has pneumonitis/interstitial lung disease. * Participant has received prior radiotherapy within 2 weeks of start of study treatment or have had a history of radiation pneumonitis. Note: Participants must have recovered from all radiation-related toxicities and not require corticosteroids \> 10 mg per day of prednisone or equivalent. A 1-week washout is permitted for palliative radiation (≤ 2 weeks of radiotherapy) to non-CNS disease. * Participant has an infection requiring systemic therapy within 14 days prior to the first dose of study intervention. * Participant has received a prior allogenic hematopoietic stem cell transplant or solid organ transplant. * Participant is expected to require another form of antineoplastic therapy while on study treatment. * Participant has had a myocardial infarction or unstable angina within 6 months prior to the start of study treatment or currently has an uncontrolled illness including, but not limited to symptomatic congestive heart failure, clinically significant cardiac disease, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Participant has inadequately controlled hypertension (defined as systolic blood pressure \>= 140 and/or diastolic blood pressure \>= 90 mmHg on antihypertensive medications, or systolic blood pressure \> 130 and/or diastolic blood pressure \> 80 mmHg without antihypertensive medications). * Participant has a corrected QT interval using Fridericia's formula (QTcF) \> 450 msec (for male and female participants) during screening. ECGs will be performed in triplicate during screening. (The average of the triplicate readings will be used in the calculation for corrected QT interval \[QTc\]). * Participant has a prior malignancy, other than the current malignancy for which the participant is seeking treatment, active (i.e., requiring treatment or intervention) within the previous 2 years except for locally curable malignancies that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer or carcinoma in situ of the cervix or breast. * Participant has had a major surgical procedure and has not completely recovered within 28 days prior to the first dose of study intervention. * Participant has a history of bleeding diathesis that makes the participant unsuitable for study participation. * Participant requires use of any anticoagulation therapy. * Participant has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the participant to participate in the study. * Participant has a known or suspected hypersensitivity to ASP1570. For participants entering combination therapy, they have a known or suspected hypersensitivity to the respective standard therapy study intervention (pembrolizumab, docetaxel, TAS 102, mFOLFOX6, FOLFIRI and/or bevacizumab), or any components of the formulation used. * For the combination therapies, participant has received radiation therapy to the lung that is \> 30 Gy within 6 months of the first dose of study intervention. * All Solid Tumors Combination Therapy Cohort only: HIV-infected participants with a history of Kaposi sarcoma and/or multicentric Castleman disease. * Dose escalation combination therapy, dose expansion combination therapy, dose expansion monotherapy, China safety lead in and backfill participants: participants with known actionable driver mutation (e.g., EGFR, ALK, NTRK). * Previous therapy with DGK inhibitor is prohibited. * Participants with a history of or ongoing sensory or motor neuropathy Grade 2 or higher. * Participants with a history of ≥ Grade 2 hearing loss (only for NSCLC \[1L\] combination therapy cohort with carboplatin).