Study of the Combination Dostarlimab With Niraparib In Patients With Penile Carcinoma

Inclusion Criteria: * Provide written, informed consent to participate in the study and follow the study procedures * Histologically confirmed stage III (unresectable) or stage IV penile cancer, as per American Joint Committee on Cancer (AJCC) staging system. * Life expectancy \>12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status of 0, or 1 (ECOG performance status 2 can be included after discussion with PI) * Measurable disease per iRECIST * Participants who have progressed or had tolerance problems to no more than one prior line of therapy in the locally advanced setting or post platinum-based chemotherapy, including in a neoadjuvant or adjuvant setting or in combination with radiation therapy. * Participants must not have received any prior immune-oncology regimens, including but not limited to checkpoint inhibitors such as anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T cell co-stimulation or checkpoint pathways, indoleamine 2,3-dioxygenase pathway inhibitors, cancer vaccines, adoptive cell therapies, or other cytokine therapies * Demonstrated adequate organ function, as defined in protocol, within 28 days of treatment initiation * Clinically significant toxic effect(s) of the most recent prior chemotherapy must be Grade 1 or resolved (except alopecia and sensory neuropathy that may be Grade 2). * If the participant received major surgery or radiation therapy of \> 30 Gy, they must have recovered from the toxicity and/or complications from the intervention. * Participants and their female partners of childbearing potential must agree and commit to use a highly effective form of contraception (e.g., condom with spermicidal foam/gel/film/cream/suppository) throughout the duration of the study until 6 months (female participants) and 3 months (male participants and their female partners), respectively, following the last dose of study drug. Female partner may use either an intrauterine device or hormonal contraception and continue until 3 months following the last dose of study drug. This criterion may be waived for male patients who have had a vasectomy 90 days months before signing the informed consent form (ICF) or a penectomy. * Participants must not have known active brain metastases. * Participants with treated brain metastases are eligible if they have neurologically returned to baseline (except for residual signs or symptoms related to the cns treatment) for at least 4 weeks prior to the first dose of study drug(s). * Participant cannot be receiving any chronic systemic steroids (prednisone or equivalent) \> 20 mg daily, for at least 4 weeks prior to the first dose of study drug(s). * Participants with small, untreated, asymptomatic central nervous system (CNS) metastases without associated edema, shift, or requirement for steroids are eligible after discussion with the Medical Monitor, i.e. the Principal Investigator. * No stereotactic radiation or craniotomy within 4 weeks of Cycle 1 Day 1 * No new central nervous system lesions on repeat radiographic imaging 4 weeks or more from last treatment * No clinically significant symptoms secondary to brain metastases * Participants must also consent to allow acquisition of existing formalin-fixed paraffin-embedded (FFPE) material (archival tumor tissue), either a block or unstained slides for planned correlative studies. Exclusion Criteria: * Use of an investigational agent or an investigational device within 4 weeks or within a time interval less than at least 5 half-lives of the investigational agent, whichever is shorter, before administration of first dose of study drug. * Active, known or suspected autoimmune disease requiring systemic treatment within the past 2 months or a documented history of clinically severe autoimmune disease that requires systemic steroids or immunosuppressive agents. (Exceptions include any patient on 10 mg or less of prednisone or equivalent, patients with vitiligo, hypothyroidism stable on hormone replacement, Type I diabetes, Graves' disease, Hashimoto's disease, alopecia areata, eczema, or with PI approval.) * History of allergy or hypersensitivity to study drug components * History of organ transplant that requires use of immune suppressive agents * Current active pneumonitis within 90 days of planned start of the study or a known history of interstitial lung disease, drug-related pneumonitis, or radiation pneumonitis requiring steroid treatment. * Prior surgery or radiotherapy encompassing \>20% of the bone marrow within 14 days of therapy. Patients must have recovered from all radiation-related toxicities. * Active infection requiring systemic therapy; a known history of active tuberculosis. * Has known active hepatitis B virus (HBV) infection (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C virus (HCV) infection (e.g., HCV ribonucleic acid \[RNA\] qualitative is detected) * Has known immunodeficiency or active human immunodeficiency virus (HIV-1/2 antibodies) with CD 4 count \< 400 for in the past 6 months. * Prolonged corrected QT interval (QTcF) \> 450 ms for men * History of unstable or deteriorating cardiac disease within the previous 6 months prior to screening including but not limited to the following: 1. Unstable angina or myocardial infarction 2. Congestive heart failure (New York Heart Association \[NYHA\] Class III or IV) 3. Uncontrolled clinically significant arrhythmias * Systolic BP \>140 mmHg or diastolic BP \>90 mmHg that has not been adequately treated or controlled. Need for \> 2 antihypertensive medications for management of hypertension (excluding diuretics) * Must not have received a transfusion (platelets or red blood cells) ' 4 weeks prior to initiating protocol therapy. * Must not have received colony stimulating factors (e.g., granulocyte colony-stimulating factor, granulocyte macrophage colony stimulating factor, or recombinant erythropoietin) within 4 weeks prior initiating protocol therapy. * Has had any known Grade 3 or 4 anemia, neutropenia or thrombocytopenia due to prior chemotherapy that persisted \> 4 weeks and was related to the most recent treatment. * Must not have any known history of myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML) * Has experienced a Grade 3 or greater immune-related Adverse Event with prior immunotherapy, with the exception of non-clinically significant lab abnormalities. * Has received a live vaccine within 30 days of initiating protocol therapy