Study of TSR-033 With an Anti-programmed Cell Death-1 Receptor (PD-1) in Participants With Advanced Solid Tumors

Inclusion Criteria for participants in Part 1: * The participant is \>=18 years of age. * The participant has any histologically or cytologically confirmed advanced (unresectable) or metastatic solid tumor and has PD after treatment with available therapies that are known to confer clinical benefit or who are intolerant to treatment. * The participant must have an archival tumor tissue sample that is formalin-fixed and paraffin-embedded (FFPE) (blocks preferred over slides) and requested and confirmed available from offsite locations prior to dosing. The quality and quantity of the sample must be confirmed sufficient as per the Study Laboratory Manual. Participants who do not have archival tissue must agree to a new biopsy to obtain fresh tumor tissue prior to dosing. * Part 1b (PK/PDy cohort): The participant must have lesions amenable for biopsy and agree to undergo biopsies for fresh tumor tissue prior to treatment, approximately 4 to 6 weeks after treatment, and, whenever possible, at the time of PD and /or end of treatment (EOT). Serial biopsies are optional for participants in Part 1a and 1c. * Female participants must have a negative serum or urine pregnancy test within 72 hours prior to the date of the first dose of study medication if of childbearing potential or be of non-childbearing potential. Non-childbearing potential is defined as: * Participants \>=45 years of age and has not had menses for \>1 year. * Amenorrheic for \<2 years without a hysterectomy and oophorectomy and a follicle-stimulating hormone value in the postmenopausal range upon pre-study (screening) evaluation. * Post hysterectomy, bilateral oophorectomy, or tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure. * Female participants of childbearing potential (that is \[ie\], those who do not meet above criteria) must agree to use 2 highly effective forms of contraception with their partners, starting with the screening visit through 150 days after the last dose of study therapy. * The participant must have an ECOG PS of \<=1. * The participant has adequate hematologic and organ function, defined as: * Absolute neutrophil count (ANC) \>=1500 per microliter (/μL). * Platelets \>=100,000/μL. * Hemoglobin (Hb) \>=9 grams per deciliter (g/dL) or \>=5.6 millimoles per liter (mmol/L). * Serum creatinine \<=1.5 times upper limit of normal (× ULN) or calculated creatinine clearance (CrCL) \>=50 milliliters per minute (mL/min) using Cockcroft-Gault equation for participants with creatinine levels \>1.5 × institutional ULN * Total bilirubin \<=1.5 × ULN and direct bilirubin \<=1× ULN (in the event that the total bilirubin result exceeds the upper institutional limits of normal, direct bilirubin will be obtained to determine eligibility). * AST and ALT \<=2.5 × ULN unless liver metastases are present, in which case they must be \<=5 × ULN. * INR of PT \<=1.5 × ULN, unless participant is receiving anticoagulant therapy, then PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants; aPTT) \<= 1.5 × ULN unless participant is receiving anticoagulant therapy, then PT or PTT is within therapeutic range of intended use of anticoagulants. Inclusion criteria for participants in Part 2: * The participant is \>= 18 years of age. * The participant has any histologically or cytologically confirmed CRC that is metastatic or not amenable to potentially curative resection (advanced), in the opinion of the Investigator. * The participant has a primary and/or metastatic tumor(s) that is known to be MSS, as determined locally. * The participant must have lesions amenable for biopsy and agree to undergo biopsies for fresh tumor tissue prior to treatment, approximately 4 to 6 weeks after, and, whenever possible, at EOT and/or the time of PD. If the participant has had a biopsy prior to entering the 28-day screening period, and within approximately 12 weeks of study treatment, that biopsy sample may be accepted as the Baseline fresh biopsy. Additionally, submission of sufficient high-quality archival tumor tissue is recommended, if available, to enable a longitudinal analysis of tumor biomarkers. * The participant has measurable disease by RECIST v1.1. * The participant has resolution to Grade \<=1, per CTCAE v5.0, of all clinically significant toxic effects of prior chemotherapy, surgery, radiotherapy, or hormonal therapy, with the exception of peripheral neuropathy, which must have resolved to Grade \<=2, and except where otherwise noted in the eligibility criteria. * Female participants must have a negative serum or urine pregnancy test within 72 hours prior to the date of the first dose of study medication if of childbearing potential or be of non-childbearing potential. Non-childbearing potential is defined as: * Participants \>=45 years of age and has not had menses for \>1 year. * Amenorrheic for \<2 years without a hysterectomy and oophorectomy and a follicle-stimulating hormone value in the postmenopausal range upon pre-study (screening) evaluation. * Post hysterectomy, bilateral oophorectomy, or tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure. * Female participants of childbearing potential (ie, those who do not meet above criteria) must agree to use 2 highly effective forms of contraception with their partners, starting with the screening visit through 150 days after the last dose of study therapy. * The participant has an ECOG PS of \<=1. * The participant has adequate hematologic and organ function, defined as: * ANC \>=1500/μL. * Platelets \>=100,000/μL. * Hb \>=9 g/dL or \>=5.6 mmol/L. * Serum creatinine \<=1.5 × ULN or calculated CrCL \>=50 mL/min using Cockcroft-Gault equation for participants with creatinine levels \>1.5 × institutional ULN * Total bilirubin \<=1.5 × ULN and direct bilirubin \<=1× ULN (in the event that the total bilirubin result exceeds the upper institutional limits of normal, direct bilirubin will be obtained to determine eligibility). * AST and ALT \<=2.5 × ULN unless liver metastases are present, in which case they must be \<=5 × ULN. * INR of PT \<=1.5 × ULN, unless participant is receiving anticoagulant therapy, then PT or PTT is within therapeutic range of intended use of anticoagulants; aPTT) \<= 1.5 × ULN unless participant is receiving anticoagulant therapy, then PT or PTT is within therapeutic range of intended use of anticoagulants. * Urinary protein is \<=1+ on dipstick for routine urinalysis; if urine protein \>=2+, a 24-hour urine sample must be collected and must demonstrate \<1000 mg of protein in 24 hours to allow participation in the study. * Baseline albumin \>=3.0 g/dL. Inclusion Criteria for participants in Part 2A: * The participant must have had at least 2, but no more than 3, prior lines of therapy in the advanced or metastatic setting. Adjuvant chemotherapy with radiographic progression \>12 months after the last dose will not be considered a line of therapy. * The participant has progressed on standard therapies or withdrawn from standard treatment due to unacceptable toxicity. Previous standard treatment must include all of the following: * Fluoropyrimidine. * Oxaliplatin: Participants treated with oxaliplatin in adjuvant setting should have progressed after 12 months of completion of adjuvant therapy or they must have been treated with oxaliplatin for metastatic disease. * Irinotecan. * Participants whose disease is known to be RAS-wild-type must have been treated with cetuximab, panitumumab, or other epidermal growth factor receptor (EGFR) inhibitor for metastatic disease. * Bevacizumab and/or another anti-angiogenic agent. * Previous treatment with regorafenib and/or TAS-102 are allowed in the absence of contraindications and if these agents are available to the participant according to local standards. * The time between a participants's last chemotherapy and enrollment must be \<=8 weeks. Inclusion Criteria for participants in Part 2B: * The participant has received \<=2 prior systemic chemotherapy regimens in any setting (only 1 prior regimen for metastatic disease is permitted). Inclusion Criteria for participants in Part 2 Cohort B1: * The participant has received first-line combination therapy consisting of bevacizumab or anti-EGFR antibodies with FOLFIRI and has experienced radiographic progression during or after first-line therapy. Radiographic progression \>12 months after the last dose of adjuvant therapy will not be considered a line of therapy. * mFOLFOX6 therapy with bevacizumab is appropriate for the participant and is recommended by the investigator. Inclusion Criteria for participants in Part 2 Cohort B2: * The participant has received first-line combination therapy consisting of bevacizumab or anti-EGFR antibodies with FOLFOX (or variant) and has experienced radiographic progression during or after first-line therapy. Radiographic progression \>12 months after the last dose of adjuvant therapy will not be considered a line of therapy. * FOLFIIRI therapy with bevacizumab is appropriate for the participant and is recommended by the investigator. Exclusion Criteria for all participants: * The participant has previously been treated with an anti-LAG-3 antibody. * The participant has known uncontrolled central nervous system (CNS) metastases and/or carcinomatous meningitis. * The participant has a known concurrent, serious, uncontrolled medical disorder, nonmalignant systemic disease, or active infection requiring systemic therapy, including human immunodeficiency virus (HIV), known active hepatitis B or hepatitis C, active infection, or active autoimmune disease. * The participant is pregnant or breastfeeding, or expecting to conceive children within the projected duration of the study. * The participant has a history of interstitial lung disease. * The participant has not recovered (ie, to Grade \<=1 or to Baseline) from radiation- and chemotherapy-induced AEs, has received transfusion of blood products (including platelets or red blood cells), or has received administration of colony stimulating factors (including granulocyte colony-stimulating factor \[G-CSF\], granulocyte macrophage colony-stimulating factor, or recombinant erythropoietin) within 3 weeks prior to the first dose of study drug. * The participant is currently participating in an investigational study (therapy or device) or has participated in an investigational study within 4 weeks prior to the first dose of study drug. * The participant has received prior anticancer therapy (chemotherapy, targeted therapies, radiotherapy, or immunotherapy) within 21 days or less than 5 times the half-life of the most recent therapy prior to the first dose of the drug, whichever is shorter. * The participant has received wide-field (full-dose pelvic) radiotherapy within 28 days prior to the first dose of study drug. * The participant has a history of uncontrolled hereditary or acquired bleeding or thrombotic disorders. * The participant has experienced any arterial thrombotic or arterial thromboembolic events, including, but not limited to myocardial infarction, transient ischemic attack, or cerebrovascular accident, within 12 months prior to first dose of study drug. * The participant has received a prior autologous or allogeneic organ or transplantation. * The participant has undergone major surgery within 28 days or subcutaneous venous access device placement within 7 days prior to the first dose of study drug. * The participant has had a serious non-healing wound, ulcer, or bone fracture within 28 days prior to first dose of study drug. * The participant has an elective or planned major surgery to be performed during the course of the trial. * The participant has a history of inflammatory bowel disease or Crohn's disease requiring medical intervention (immunomodulatory or immunosuppressive medications or surgery) in the 12 months prior to the first dose of study drug. * The participant has an acute or subacute bowel obstruction, abdominal fistula, or history of chronic diarrhea which is considered clinically significant, in the opinion of the investigator. * The participant has experienced a Grade \>=3 bleeding event within 3 months prior to the first dose of study drug. * The participant has either peptic ulcer disease associated with a bleeding event or known active diverticulitis. * The participant has not recovered (Grade \>=1) from AEs and/or complications from any major surgery prior to the first dose of study drug. * The participant has received a vaccine within 7 days of the first dose of study drug. * The participant has known hypersensitivity to TSR-033, dostarlimab (Part 1c and Part 2), or associated excipients. Exclusion Criteria for participants in Part 1: * The participant's prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, or anti-LAG-3 agent that resulted in permanent discontinuation due to an AE. Exclusion Criteria for participants in Part 2: * The participant has been previously treated with an anti-PD-1 or anti-PD-L1 antibody. Exclusion Criteria for participants in Part 2B: * The participant has known dihydropyrimidine dehydrogenase deficiency. * The participant experienced an arterial thrombotic/thromboembolic event, Grade 4 hypertension, Grade 4 proteinuria, a Grade 3-4 bleeding event, or bowel perforation during first-line therapy with a bevacizumab-containing regimen. * The participant has known hypersensitivity to bevacizumab, mFOLFOLX6 (Cohort B1) or FOLFIRI (Cohort B2), or associated excipients. * The participant experienced PD within 12 months of last dose of adjuvant therapy.