Vevorisertib (ARQ 751) as a Single Agent or in Combination With Other Anti-Cancer Agents, in Solid Tumors With PIK3CA / AKT / PTEN Mutations (MK-4440-001)

Inclusion Criteria 1. Signed written informed consent granted prior to initiation of any study-specific procedures 2. 18 years of age and older 3. Histologically and/or cytologically documented diagnosis of a selected tumor type that is locally advanced, inoperable, metastatic or recurrent (including but not restricted to breast cancer, TNBC \[triple negative\]; HR-positive \[HR+\]/HER2-negative \[HER2-\] or endometrial cancer) 4. Documented AKT genetic alterations or known actionable PIK3CA/PTEN mutations by genetic testing • Participants with tumors with PTEN null/PTEN loss-of-function mutations are not eligible 5. For combination arms; participants should be eligible for paclitaxel or fulvestrant therapy as per Investigator assessment 6. Failure to respond to standard systemic therapy, or for whom standard or curative systemic therapy does not exist or is not tolerable * Participants in single agent arm (with AKT genetic alterations) and participants in dose escalation cohorts of combination therapy arms should have at least one line of standard systemic therapy * Participants in single agent arm (with PIK3CA/PTEN actionable mutations) and participants in the expansion cohorts of combination therapy arms should have no more than 3 prior systemic regimens for the advanced disease * Neoadjuvant and adjuvant chemotherapy are considered one regimen if they are a continuation of the same regimen with interval debulking surgery * If the participant is refractory or has disease progression within 6 months after completion of the adjuvant treatment, then the adjuvant treatment should be considered as the line of treatment rather than an adjuvant therapy. * Endocrine (hormonal) therapy does not count toward total lines of therapy * Maintenance therapy is considered part of the preceding regimen if one or more of the same drugs are continued 7. Has at least one measurable target lesion according to RECIST v. 1.1 8. Eastern Cooperative Oncology Group (ECOG) performance status (PS) ≤ 1 9. Adequate organ function as indicated by the following laboratory values. (All laboratory tests must be obtained within 14 days prior to the first dose of study treatment): 1. Hematological * Absolute neutrophil count (ANC) ≥ 1.5 x 10⁹/L * Platelet count (Plt) ≥ 100 x 10⁹/L * Hemoglobin (Hb) ≥ 9 g/dL * International normalized ratio (INR) 0.8 to upper limit of normal (ULN) or ≤ 3 for participants receiving anticoagulant therapy such as Coumadin or heparin 2. Renal * Serum creatinine ≤ 1.5 x ULN or calculated creatinine clearance ≥ 60 mL/min/1.73 m2 for participants with serum creatinine levels \> 1.5 x institutional ULN 3. Hepatic * Total bilirubin ≤ 1.5 x ULN * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3 x ULN or ≤ 5 x ULN for participants with known liver metastases 4. Metabolic * Glycated hemoglobin (HbA1c) ≤ 8% (≤ 64 mmol/mol) 10. If a participant is currently receiving bisphosphonates or any other drug for treatment of osteoporosis, treatment-induced bone loss and metastases to bone, the participant must have received the bisphosphonates for at least four weeks prior to the first dose of study treatment • Initiation of bisphosphonates or similar agents during the study may be allowed provided the participant completes the first cycle of treatment without any dose limiting toxicity (DLT) and the Investigator rules out tumor progression 11. Male or female participants of child-producing potential must agree to use adequate contraception, including double-barrier contraceptive measures, oral contraception, or avoidance of intercourse during the study and for 90 days after the last dose of study treatment 12. Women of childbearing potential must have a negative serum pregnancy test. "Women of childbearing potential" is defined as sexually mature women who have not undergone a hysterectomy or who have not been naturally postmenopausal for at least 12 consecutive months prior to the first dose of study treatment Exclusion Criteria 1. Anti-cancer therapy, such as chemotherapy, immunotherapy, hormonal therapy, targeted therapy, or investigational agents within five half-lives or four weeks, whichever is shorter, prior to administration of the first dose of study treatment * To be eligible for study treatment, toxicity from prior treatment(s) must recover to Grade ≤ 1, except for alopecia * Concurrent systemic high-dose corticosteroids (in dosing exceeding 10 mg QD of prednisone equivalent) when used intermittently in an antiemetic regimen, for central nervous system (CNS) metastases management, or as a part of the premedication regimen are allowed 2. Radiation therapy within four weeks, or palliative radiation therapy within two weeks, prior to administration of the first dose of study treatment * To be eligible for study treatment, radiation therapy-related toxicity must recover to Grade ≤ 1 prior to administration of the first dose of study treatment * Concurrent palliative radiotherapy for local pain-control or prevention of fracture (for known bone metastases) may be allowed provided the participant completes the first cycle of treatment, does not meet criteria of progressive disease, and treated lesions will not be included in the target/non-target lesion assessment 3. Major surgical procedure within four weeks prior to administration of the first dose of study treatment • To be eligible for the study treatment, all surgical wounds must be fully healed, and any surgery-related adverse events must recover to Grade ≤ 1. 4. Unable or unwilling to swallow the complete daily dose of vevorisertib 5. Previous treatment with * AKT inhibitors (e.g., ARQ 092, MK-2206, GSK2141795, AZD5363; prior treatment with PI3K or mammalian target of rapamycin (mTOR) inhibitor are allowed) * Prior taxane therapy for the advanced, metastatic disease (for participants considered for vevorisertib +paclitaxel combination arm only) 6. Known prior allergic reaction to or severe intolerance of paclitaxel or fulvestrant. Intolerance is defined as a serious adverse event (AE), a grade 3 or 4 AE per Common Terminology Criteria for Adverse Events (CTCAE) v.4.03, or permanent treatment discontinuation 7. History of Type 1 diabetes mellitus or Type 2 diabetes mellitus requiring regular medication (other than oral hypoglycemic agents) or fasting glucose ≥ 160 mg/dL at Screening visit 8. Significant gastrointestinal disorder(s) that could, in the opinion of the Investigator, interfere with the absorption, metabolism, or excretion of vevorisertib (e.g., inflammatory bowel disease, Crohn's disease, ulcerative colitis, extensive gastric resection) 9. Known untreated or active CNS metastases and/or carcinomatous meningitis • To be eligible for the study treatment, participants must have stable disease ≥ 1 month, confirmed by magnetic resonance imaging (MRI) or computed tomography (CT) scan, and have CNS metastases well controlled by low-dose steroids, anti-epileptics, or other symptom-relieving medications 10. History of myocardial infarction (MI) or New York Heart Association (NYHA) Class II-IV congestive heart failure within 6 months of the administration of the first dose of study treatment (MI occurring \> 6 months of the first dose of study treatment will be permitted); Grade 2 or worse conduction defect (e.g., right or left bundle branch block) 11. A heart rate corrected QT (QTc) interval ≥ 480 msec, using the Fridericia's formula QTcF 12. Left ventricular ejection fraction (LVEF) \<50% as determined by Multiple Gated Acquisition (MUGA) scan or echocardiogram (ECHO) in participants who received prior treatment with anthracyclines 13. Concurrent severe and/or uncontrolled illness not related to cancer and/or social situation that would limit compliance with study requirements, including but not limited to: * Psychiatric illness, substance abuse * Ongoing or active known infection, including human immunodeficiency virus (HIV) infection, hepatitis B or C virus * Significant pulmonary dysfunction, including pneumonitis, interstitial lung disease (ILD), idiopathic pulmonary fibrosis, cystic fibrosis, severe chronic obstructive pulmonary disease (COPD) * Peripheral neuropathy grade ≥2 (vevorisertib+paclitaxel combination arm) * Bleeding diathesis, thrombocytopenia or coagulation disorders (vevorisertib+fulvestrant combination arm) * Thrombotic/coagulation disorders within 6 months prior to the first dose of study treatment unless stable on anticoagulation for \> 3 months 14. Active or history of other malignancy other than the current cancer within 2 years of the first dose of study treatment, with the exception of carcinoma in-situ of the cervix, basal cell carcinoma, and superficial bladder tumors curatively treated 15. Blood transfusion or administration of growth factors within 5 days prior to a blood draw being used to confirm eligibility 16. Pregnant or breastfeeding