Study of TSR-042, an Anti-programmed Cell Death-1 Receptor (PD-1) Monoclonal Antibody, in Participants With Advanced Solid Tumors

Inclusion Criteria: * Participant is at least 18 years of age. * Participant has proven recurrent or advanced solid tumor and has disease progression after treatment with available anticancer therapies, or is intolerant to treatment that meets the following requirements for the part of the study they will participate in: A. Part 1: Any histologically or cytologically proven recurrent or advanced solid tumor B. Part 2A: : Any histologically or cytologically proven recurrent or advanced solid tumor C. Part 2B: Histologically of cytologically proven recurrent or advanced solid tumor with measurable lesion(s) per RECIST version 1.1 and meets one of the following disease types: The criteria below should be met for participant participating in: 1) Cohort A1 (dMMR/MSI-H endometrial cancer) and 2) Cohort A2 (MMR-proficient/MSS endometrial cancer) * Participants who have progressed on or after platinum doublet therapy * Participants have received no more than 2 lines of anticancer therapy for recurrent or advanced (\>=Stage IIIB) disease. Prior treatment with hormone therapies is acceptable and does not count towards the number of anticancer therapies noted in the criterion above for this cohort. * All endometrial cancer histologies are allowed except endometrial sarcoma (including carcinosarcoma). * Participants must submit 2 scans demonstrating increase in tumor measurement that meet criteria for PD on or after the latest systemic anticancer therapy based on RECIST Version 1.1 to Central Radiology prior to the first dose of dostarlimab. * Presence of at least 1 measurable lesion on Baseline scan will be confirmed by central radiology review. * Status of tumor MMR/MSI: Participants can be screened based on local MMR/MSI testing results using immunohistochemistry (IHC), polymerase chain reaction (PCR), or next generation sequencing (NGS) performed in a certified local laboratory, but participant eligibility needs to be determined by MMR IHC results. For participant with available local MMR IHC results for the respective cohort(s), tumor samples have to be submitted to a central IHC laboratory and its quality has to be checked and cleared prior to Cycle 1 Day 1 (C1D1). For participants without available local MMR IHC test results (participants with local PCR or NGS test results), central IHC results have to confirm eligibility prior to proceeding with other screening procedures. After the central IHC test is completed, remaining tumor tissue may be tested for further exploratory biomarkers or may be sent to a central NGS laboratory for further testing. 3\) Cohort E - Participants with NSCLC who progressed after at least 1 prior platinum-based systemic chemotherapy regimen for recurrent or advanced disease. * Chemotherapy regimen in the adjuvant or neoadjuvant setting following surgery and/or radiation is acceptable if recurrent or advanced disease develops within 6 months from completion of therapy. * Participants with a known epidermal growth factor receptor (EGFR) mutation must have received a chemotherapy regimen and an EGFR tyrosine kinase inhibitor (TKI) (e.g., erlotinib, gefitinib, afatinib, or experimental) * Participants with a known anaplastic lymphoma kinase (ALK) translocation must have received a chemotherapy regimen and an ALK inhibitor (e.g., crizotinib, ceritinib or experimental) 4) Cohort F - Participants with recurrent or advanced dMMR/MSI-H solid tumors except endometrial cancers and gastrointestinal cancers, who have received prior systemic therapy and who have no alternative treatment options. Prior treatment with hormone therapies alone given for recurrent or advanced disease is acceptable. * Presence of at least 1 measurable lesion by RECIST 1.1 on baseline scan will be confirmed by central radiology review prior to first dose of dostarlimab. Patients with primary central nervous system (CNS) tumor should provide brain MRI at baseline. * Presence of deficient mismatch repair (dMMR) and/or microsatellite instability (MSI-H) in the tumor defined by either: i) deficient DNA mismatch repair (dMMR); MMR status must be assessed by immunohistochemistry (IHC) for MMR protein expression (MLH1, MSH2, MSH6, PMS2) where loss of one or more proteins indicates dMMR; dMMR may be determined either locally or by the central reference lab; OR ii) Microsatellite instability (MSI-H); MSI-H as determined by polymerase chain reaction (PCR) or by tissue NGS; MSI-H may be determined locally 5) Cohort G: Participants must have recurrent high-grade serous, endometrioid, or clear cell ovarian, fallopian tube, or primary peritoneal cancer. * Participants must have presence of at least 1 measurable lesion on Baseline scan that will be confirmed by central radiology review. * Participants must be considered resistant to the last administered platinum therapy, that is, the time from the last administered platinum dose until the initial documented progression (as evidenced by radiographic progression per RECIST version 1.1) must be less than 6 months. * Participants must have completed at least 1 but no more than 3 prior lines of therapy for advanced or metastatic ovarian cancer. Neoadjuvant, adjuvant, and the combination of both will be considered as 1 line of therapy. Treatment with single-agent bevacizumab given as maintenance is not counted as a separate line of therapy. If a therapeutic regimen is modified or changed for a reason other than lack of response or PD (such as allergic reaction, toxicity, or drug availability), this is not counted as a separate line of therapy. The use of single-agent hormonal therapy given for reasons other than PD per RECIST version v1.1 (i.e., hormonal therapy given for increasing Cancer antigen \[CA\]-125 levels) is not counted as a separate line of therapy. * Participants must have been previously treated with platinum-based regimn, taxane agent(s), and bevacizumab (bevacizumab could be used as a single agent or in combination with another agent, in frontline therapy, as maintenance, or for treatment of recurrent disease). • Part 2B: Participants must have archival tumor tissue available that is formalin-fixed and paraffin-embedded (FFPE). * For participants who do not have archival tissue, a new biopsy must be performed to obtain a tissue sample prior to study treatment initiation. For participants without available archival tissue, the biopsy should be taken from the tumor lesions (either primary or metastatic) that have easy accessibility and low biopsy-associated risks and will exclude biopsies of the liver, brain, lung/mediastinum, pancreas, or endoscopic procedures extending beyond the esophagus, stomach or bowel. * For Cohort F an FFPE tissue sample must be submitted to the central laboratory for testing. Specimens containing bone are not acceptable. For patients with available local MMR/MSI-H results, tumor samples have to be submitted to a central laboratory and its quality has to be checked and cleared prior to C1D1 * For Cohort G, participant must provide formalin fixed paraffin embedded (FFPE) tumor tissue block(s) with sufficient tumor content (as confirmed by the Sponsor's designated central laboratory) during screening to enable, for example, measures of homologous recombination pathway defects and PD-L1 status. The use of slides created from paraffin-embedded tissue as opposed to FFPE blocks must be approved by the Sponsor. • Female participants must have a negative serum pregnancy test within 72 hours prior to the date of the first dose of study medication: unless they are of non-child bearing potential.Non child bearing potential is defined as: * \>= 45 years of age and has not had menses for \> 1 year; * Amenorrheic for \< 2 years without a hysterectomy and oophorectomy and have a follicle- stimulating hormone (FSH) value in the postmenopausal range upon pre-study (screening) evaluation. * Post-hysterectomy, post-bilateral oophorectomy, or post-tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound, magnetic resonance imaging (MRI) or computed tomography (CT) scan. Tubal ligation must be confirmed with medical records of the actual procedure. * Female participants of childbearing potential must agree to use 1 highly effective form of contraception with their partner starting with the screening visit through 150 days after the last dose of study therapy. * Participant has an Eastern Cooperative Oncology Group (ECOG) performance status of \<= 2 for Part 1 and \<= 1 for Part 2. * Participant has an adequate organ function. * Participants with known human immunodeficiency virus (HIV) infection are allowed with following requirements: * Documented evidence of plasma HIV-1 RNA persistently \<50 copies (c)/mL ≤3 months prior to AND at Screening. In the \>3 to 12 months prior to Screening, plasma HIV-1 RNA consistently \<50 c/mL required; if single increases ≥50 c/mL occurred, they cannot have been persistent nor associated with antiretroviral resistance per Investigator's assessment AND * CD4 cell count \>350 cells/mm\^3 over past 12 months and at Screening (and no measurement ≤200 cells/mm3 during that time period) AND * Must be on an uninterrupted combination antiretroviral therapy regimen for at least 3 months prior to Screening, with combination antiretroviral therapy regimen consistent with locally recommended guidelines * Participants with history of Centers for Disease Control and Prevention (CDC) Stage 3 disease (CDC, 2014; also known as acquired immunodeficiency syndrome \[AIDS\]- defining disease) are allowed if AIDS-defining disease has been treated and cured or is stable for ≥3 months prior to study entry. Cutaneous Kaposi's Sarcoma not requiring systemic therapy is allowed. * No history of HIV-associated non-Hodgkin lymphoma ≤5 years prior to study and no history of HIV-associated invasive cervical cancer * No treatment with an HIV-1 immunotherapeutic vaccine within 90 days of Screening. Exclusion Criteria: * Participant has received prior therapy with an anti- programmed death receptor 1 (anti-PD-1), anti-PD-1- ligand-1 (anti-PD-L1), or anti-PD-1 ligand-2 (anti-PD- L2) agent. * Participant has a known uncontrolled CNS metastasis and/or carcinomatous meningitis. * Participant has a known additional malignancy that progressed or required active treatment within the last 2 years. Exceptions include basal cell carcinoma of the skin, squamous cell cancer (SqCC) of the skin that has undergone potentially curative therapy, or in situ cervical cancer, or other neoplastic condition which has undergone curative therapy and is considered cured by the investigator. * Participant is considered a poor medical risk due to a serious, uncontrolled medical disorder, nonmalignant systemic disease or active infection requiring systemic therapy. Specific examples include, but are not limited to, active, non-infectious pneumonitis; uncontrolled ventricular arrhythmia; recent (within 90 days) myocardial infarction; uncontrolled major seizure disorder; unstable spinal cord compression; superior vena cava syndrome; or any psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study (including obtaining informed consent). * Participant is pregnant or breastfeeding or expecting to conceive children within the projected duration of the study, starting with the Screening Visit through 150 days after the last dose of study treatment. * Participant has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment. * Participant has a documented presence of hepatitis B surface antigen \[HBsAg\] at screening or within 3 months prior to the first dose of study intervention. Participants with a negative HbsAg and positive hepatitis B virus core antibody (HBcAb) result are eligible only if HBV DNA is negative. * Participant has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease- modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. Use of inhaled steroids, local injection of steroids, and steroid eye drops are allowed. * Participant has as history of interstitial lung disease. * Participant has not recovered (i.e., to \<= Grade 1 or to Baseline) from radiation- and chemotherapy-induced AEs or received transfusion of blood products (including platelets or red blood cells) or administration of colony-stimulating factors (including granulocyte-colony stimulating factor \[G-CSF\], granulocyte macrophage colony-stimulating factor \[GM-CSF\] or recombinant erythropoietin) within 3 weeks prior to the first dose of study drug. * Participant has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks prior to the first dose of study drug. * Participant has received prior anticancer therapy (chemotherapy, targeted therapies, radiotherapy, or immunotherapy) within 21 days prior to study Day 1 * Participant has not recovered adequately (\<= Grade 1) from AEs and/or complications from any major surgery prior to starting therapy. * Participant has received a live vaccine within 14 days of planned start of study therapy. * Participant has a known hypersensitivity to dostarlimab components or excipients. * For Cohort G, participants will not be eligible if they meet the following criteria: * Participants who experienced disease progression within 3 months (as evidenced by radiographic progression per RECIST) of first-line platinum therapy. * Participants with known deleterious or suspicious deleterious mutation in BRCA1 or BRCA2 genes (local testing permitted). * Participants has received prior therapy with a poly(adenosine diphosphate-ribose) polymerase (PARP)-1/PARP-2 inhibitor. * Participant has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, might interfere with the participant's participation for the full duration of the study treatment, or is not in the best interest of the participant to participate. * Participant is immunocompromised. Participants with splenectomy are allowed.