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

Immune therapies work with the body's immune system to treat a number of cancers. They work with T-cells, a type of white blood cell, to target and attack specific tumors. However, some tumors can become resistant to attack by T-cells over time. They do this by sending "off" signals to T-cells. The researchers are finding ways to switch the T-cells back on. Before a treatment can be approved for use, clinical studies need to be done. This study will provide more information on ASP1570 in adults with advanced solid tumors. ASP1570 will either be given by itself, or given with another medicine called pembrolizumab, given with a standard cancer therapy, or given together with pembrolizumab and other medicines called pemetrexed and carboplatin. The main aims of this study are： * To check the safety of ASP1570 * To check how well ASP1570 is tolerated * To find a suitable dose of ASP1570 This study is for adults with advanced solid tumors. Their tumor has either grown outside of the area where it started (locally advanced and unresectable) or it has spread to other parts of the body (metastatic). Their cancer gets worse after standard therapy or they are unable to have standard therapy. The study doctors can give more advice about who can take part. This study will be in 2 parts. In Part 1, the most suitable dose of ASP1570 to give to people with advanced solid tumors will be worked out. Different small groups of people with advanced solid tumors will take lower to higher doses of ASP1570. People will either be given ASP1570 by itself, or ASP1570 with pembrolizumab, ASP1570 with a standard cancer therapy, or ASP1570 with pembrolizumab, pemetrexed and carboplatin. The study treatment given depends on the type of cancer people have. There are different doses of ASP1570, with each group staying on the same dose. There is just 1 standard dose of pembrolizumab. The dose of a standard cancer therapy depends on its label. After taking the lowest dose of ASP1570, the first group will be checked for medical problems. The next group can only take the higher dose of ASP1570 if the first group tolerates the lowest dose. This will continue in the same way for each group. Each group will take tablets of ASP1570 either once or twice every day in a 21-day cycle. People will continue with more treatment cycles on the same dose unless they can't tolerate the study treatment, their cancer gets worse or the study doctor decides that person should stop treatment. People who also receive treatment with pembrolizumab will be infused with pembrolizumab on the first day of every other cycle of ASP1570 (once every 6 weeks). People who are receiving a standard cancer therapy (with ASP1570) will be treated according to its label. In Part 2, different small groups of people with advanced solid tumors will take the most suitable dose of ASP1570 worked out from Part 1. The dose will not go above the highest dose that people could tolerate from Part 1. ASP1570 will be given either once a day or twice a day in a 21-day cycle. Pembrolizumab will be given once every 6 weeks. Other study treatments will be given in 14-day, 21-day or 28-day cycles. The cycle length and other study treatments given (pembrolizumab and the type of standard cancer therapy will depend on what type of tumor people have. The standard cancer therapies will be given according to their label. All groups will continue with more treatment cycles with ASP1570 (by itself with pembrolizumab, with a standard cancer therapy, or with pembrolizumab, pemetrexed and carboplatin) unless they can't tolerate the study treatment, their cancer gets worse or the study doctor decides that person should stop treatment.

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) \ 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).