A Study of Cobolimab Plus Dostarlimab in Pediatric and Young Adult Participants With Cancer

Inclusion Criteria: Participants are eligible to be included in the study only if all of the following criteria apply: * Participants between the age of 0 to not more than 21 years at the time of signing informed consent form (ICF). * Disease characteristics: Part 1: Participants with advanced or metastatic solid tumors who have had disease progression after treatment with available therapies that are known to confer clinical benefit and who have limited available treatment options as determined by the investigator. Additionally, exposure to prior immunotherapy or experimental therapies is acceptable: 1. Melanoma 2. Hodgkin Lymphoma 3. High and Low Grade Glioma: including Glioblastoma multiforme (GBM), Diffuse intrinsic pontine glioma (DIPG), and ependymoma. 4. Osteosarcoma 5. Hepatic tumors \[including Hepatoblastoma, Hepatocellular carcinoma (HCC), and Fibrolamellar carcinoma\] 6. Rhabdomyosarcoma Part 2: 1. Participants with Melanoma who have not received prior systemic therapy: * Participants with BRAF gene, found on chromosome 7 (BRAF) mutations who are eligible for a BRAF-targeted therapy are eligible if they qualify for immunotherapy. * Participants with locally treated and controlled metastatic central nervous system (CNS) lesions without leptomeningeal spread are eligible 2. Relapsed/refractory Hodgkin lymphoma (HL) that has failed at least 2 prior lines of systemic therapy) * Participants must have performance status \>=60 percent (%) on the Karnofsky scale for participants \>16 years of age and \>=60% on the Lansky scale for participants \<=16 years of age. * Adequate organ function as demonstrated by a complete blood count at screening obtained without transfusion \[platelets or red blood cells (RBC)\] or receipt of Colony stimulating factor (CSF), Granulocyte colony stimulating factor (G-CSF), Granulocyte macrophage colony stimulating factor (GMCSF) or rErythropoeitin (rEPO) within 2 weeks prior to screening. * Adolescent participants who have entered puberty must consent (be willing) to use of contraceptive measures, or refrain from sexual intercourse, if in line with their usual practice, as well as sperm/egg donation for the duration of treatment Exclusion Criteria: Participants are excluded from the study if any of the following criteria apply: Medical conditions: * Participant has uncontrolled CNS involvement by any tumor pathology * Participant has a heart rate-corrected QT interval according to QT interval (corrected) (Friderecia's formula) (QTcF) prolongation at screening \>470 millisecond (msec) or \>480 msec for participants with bundle branch block. * Participant has clinically significant cardiovascular disease * Participant has chronic respiratory disease * Participant has known sensitivity to study intervention components or excipients or other allergy that, in the opinion of the investigator or medical monitor, contraindicates participation in the study. * Participants who have a history of immunodeficiency disease, including other acquired or congenital immunodeficiency diseases, or organ transplantation * Participants who have received plasma exchange within 7 days before the first dose of study intervention. * Participant has current active pneumonitis or any history of pneumonitis requiring steroids or immunomodulatory treatment within 90 days of planned enrollment or any history of drug-induced pneumonitis. * Participant has a history of autoimmune disease that has required systemic treatments in the 2 years prior to screening. Participants with prior history of autoimmune disease must be discussed with the medical monitor. Replacement therapy is not considered a form of systemic therapy (e.g., thyroid hormone for autoimmune thyroiditis or insulin is not exclusionary) * Participant has ongoing adverse reaction(s) from prior therapy that has (have) not recovered to ≤Grade 1 or to the Baseline status preceding prior therapy, excluding \[e.g., alopecia, hearing loss, vitiligo, endocrinopathy managed with replacement therapy, and Grade 2 neuropathy\], or that the investigator, with the agreement of the sponsor, considers to be not clinically relevant for the tolerability of study intervention in the current clinical study. * Participant has any active renal condition (e.g., infection, requirement for dialysis, or any other significant renal condition (that could affect the participant's safety). * Participant has any serious and/or unstable medical or psychiatric disorder or other condition(s) (including laboratory assessment abnormalities) that could interfere with the participant's safety, obtainment of informed consent, or compliance to the study procedures. Prior/ Concomitant therapy: * Has received treatment with an investigational agent or any other anti-cancer therapy within 30 days, or \<5 times the half-life of the most recent therapy prior to signing ICF, whichever is shorter. * Has received systemic steroid therapy within 3 days prior to the first dose of the study treatment or is receiving any other form of immunosuppressive medication. Replacement therapy is not considered a form of systemic therapy. Use of inhaled corticosteroids, local steroid injection, or steroid eye drops is allowed. * Has not met the following waiting/washout periods for X-ray therapy (XRT) including external beam radiation therapy/external beam irradiation including protons: * Participant has had major surgery within 28 days prior to the first dose of study treatment or has not adequately recovered from any AEs (Grade ≤1) and/or complications from any major surgery. Surgical implantation of a port catheter is not exclusionary. * Prior Bone Marrow Transplant \<60 days of screening. * Participant has experienced Grade 3 or higher hypersensitivity to prior monoclonal antibody therapy. Prior/Concurrent clinical study experience * Is currently enrolled or has participated in any other clinical study involving an investigational study or interventional medical research within 21 days or 5 half-lives, whichever is shorter, of an investigational medicinal product before signing ICF Diagnostic assessments * Has documented presence of Hepatitis B surface antigen (HbsAg) at Screening or within 3 months prior to first dose of study intervention. * Has a positive Hepatitis C virus (HCV) antibody test result at Screening or within 3 months prior to first dose of study intervention. * Has a positive HCV Ribonucleic Acid (RNA) test result at Screening or within 3 months prior to first dose of study intervention. * Has a known history of Human immunodeficiency virus (HIV) or has a HIV-positive test result at Screening. * Is pregnant or breastfeeding.