PDS01ADC and M7824 for Advanced Kaposi Sarcoma

* INCLUSION CRITERIA: * Individuals with biopsy proven (confirmed in the Laboratory of Pathology \[LP\], CCR) Kaposi sarcoma (KS) * KS requiring systemic therapy, with or without history of prior KS therapy: * T1 KS or T0 KS sufficiently widespread that systemic therapy is advisable, or KS affecting quality-of-life due to local symptoms or psychological distress OR, * KS with an inadequate response to liposomal doxorubicin, paclitaxel, other systemic chemotherapy (either progressive disease or stable disease after 3 or more cycles) or immunotherapy (progressive disease) * A wash-out period off treatment of 2 weeks from last chemotherapy and 4 weeks from last immunotherapy, other systemic treatment with a biologic agent, or monoclonal antibody therapy will be required in individuals with prior KS therapy. * Resolution of toxicity from prior therapy to \<= Grade 1. * At least five measurable cutaneous KS lesions with no previous local radiation, surgical or intralesional cytotoxic therapy that would prevent response assessment for that lesion. * Measurable disease by the criteria proposed by the AIDS Clinical Trials Group (ACTG) Oncology Committee for KS * HIV positive or negative. * ART for HIV+ individuals for 8 or more weeks prior to entry with an HIV viral load of \<400 copies/ml at screening and CD4+ T cell count of \>= 50 cells/microliter as this may be expected if individuals have received several courses of chemotherapy. * Age \>=18 years. * ECOG performance status \<=2 (Karnofsky \>=60%). * Adequate organ and marrow function as defined below: * Absolute neutrophil count \>=1,000/mcL * Platelets \>=100,000/mcL * Total bilirubin within normal institutional limits; OR \<3x institutional upper limit of normal (ULN) for Gilbert s syndrome or HIV protease inhibitors; OR \<5x ULN and direct bilirubin \< 0.7mg/dL for individuals on atazanavir-containing HIV regimen * AST/ALT \<=1.5 X institutional ULN * Hemoglobin \>= 9g/dL * Creatinine within normal institutional limits OR creatinine clearance \>30 mL/min/1.73m\^2 as estimated by either Cockroft-Gault of 24- hour urine collection if creatinine levels above institutional normal * Normal international normalized ratio (INR), prothrombin time (PT) \<= 1.5 x ULN, and activated partial thromboplastin time (aPTT) \<= 1.5 x ULN (required only if participants will receive M7824) * The effects of PDS01ADC and M7824 on the developing human fetus are unknown. For this reason, women of child-bearing potential (WOCBP) and individuals able to father a child must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, during treatment and for at least 4 months after the last dose of treatment and agree to inform the treating physician immediately if they become pregnant. Also, there is unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with M7824 and/or PDS01ADC, therefore WOCBP must agree to discontinue nursing if treated with these agents. * Ability of individual to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: * Receiving any other investigational agents. * Pregnant individuals are excluded from this study as the effects of PDS01ADC and M7824 have potential teratogenic or abortifacient effects. * Severe KS (such as symptomatic pulmonary KS) that could be life threatening if it progressed over 2-4 weeks * Actively bleeding sites caused by visceral KS. * Unwilling to accept blood products as medically indicated * Actively bleeding and/or requiring transfusions in the 2 weeks preceding study entry. * History of bleeding, diathesis, or recent major bleeding events within a period of 4 weeks considered by the investigator as high risk for investigational drug treatment. * Any active or recent history (symptomatic in the last 3 months) of a known or suspected autoimmune disease (with the exception of diabetes type I, vitiligo, psoriasis, or hypo- or hyperthyroid diseases not requiring immunosuppressive treatment) or recent history of a syndrome that required systemic corticosteroids (10mg daily prednisone or equivalent) or immunosuppressive medications except inhaled steroids and adrenal replacement steroids doses up to 10mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. * Uncontrolled opportunistic infections * Active multicentric Castleman disease * Individuals with primary effusion lymphoma * History of malignant tumors other than KS, unless: * In complete remission for \>= 3 years from the time complete remission was first documented or * Resected basal cell or squamous cell carcinoma of the skin or * In situ cervical or anal dysplasia * History of allergic reactions attributed to compounds of similar chemical or biologic composition to PDS01ADC and/or M7824 investigational agents used in study. * Active tuberculosis (TB): * Individuals who are undergoing first month of therapy (RIPE or equivalent) for active TB or * Individuals with TB immune reconstitution syndrome (IRIS) requiring corticosteroids * Received or will receive a live vaccine within 30 days prior to the first administration of study intervention. Seasonal flu vaccines that do not contain a live virus are permitted. Locally approved COVID vaccines are permitted. * Uncontrolled substantial intercurrent illness including, but not limited to, ongoing or active severe infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, that would limit compliance with study requirements. * Medical or psychiatric illness or social situation that would, in the opinion of the investigator, preclude participation in the study or the ability of individuals to provide informed consent for themselves. * Uncontrolled HBV infection, defined as plasma HBV DNA detectable by PCR Note: the following will NOT be exclusionary: * A positive hepatitis B serology indicative of previous immunization (i.e. HbsAb positive and HbcAb negative), or a fully resolved acute HBV infection * Chronic HBV suppressed by appropriate antiretroviral therapy with activity against HBV, as outlined in DHHS guidelines. * Uncontrolled HCV infection, defined as plasma HCV DNA detectable by PCR Note: the following will NOT be exclusionary: * Positive HCV serology but no detectable HCV RNA, indicative of spontaneously cleared HCV infection * Successfully treated for HCV as long as therapy for HCV has been completed. -Individuals will be excluded from the combination therapy arm if: * they have discontinued prior PD1/L1 blocking agent due to immune mediated adverse event(s) OR * they have active non-infectious pneumonitis or a history of steroid requiring non-infectious pneumonitis.