PDS01ADC Monotherapy and in Combination With M7824 in Advanced Kaposi Sarcoma

Background: Kaposi sarcoma (KS) tumors grow on the skin, lymph nodes, lungs, bone, and gastrointestinal tract. KS often affects people with immune deficiencies, such as among people living with HIV or those with prior history of transplant. Researchers want to see if 2 non-chemotherapy drugs can help people with KS. PDS01ADC triggers the immune system to fight tumors. M7824 blocks the pathways that cancer cells use to stop the immune system from fighting tumors. Objective: To learn if giving PDS01ADC alone or with M7824 could help the immune system fight KS tumors. Eligibility: People 18 and older with KS that has been treated with chemotherapy or immunotherapy Design: Participants will be screened with some or all of the following: medical history physical exam chest X-ray computed tomography scan blood and urine tests electrocardiogram and echocardiogram skin KS lesion biopsy lung exam gastrointestinal exam All participants will get PDS01ADC every 4 weeks for up to 96 weeks (or 24cycles). It is injected under the skin. Some participants will also get M7824 every 2 weeks for up to 96 weeks (or 24cycles). It is given through a plastic tube that is put in an arm vein. Participants will complete questionnaires about how KS affects their quality of life. Their KS lesions will be measured and photographed. They will repeat some of the screening tests. They will give saliva samples or additional tissue samples. They will have a lung function test. Their ability to perform their normal activities will be assessed. The treatment duration is up to 96 weeks (or 24cycles) with an option to take PDS01ADC and/or M7824 until the KS tumors are not responding, or you develop unacceptable side effects. Participants will have follow-up visits 7 and 30 days after treatment ends, then every 3 to 6 months for the next 18 months, then once a year for 3 years.

* 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 \=18 years. * ECOG performance status \=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 \