Recombinant Glycosylated Human Interleukin-7 (CYT107) for the Treatment of Kaposi Sarcoma in Participants With HIV and Immune Non-Response (REGIMENKS HIV)

* INCLUSION CRITERIA: * Histologically confirmed KS by NCI Laboratory of Pathology (LP), with or without any prior systemic KS treatment * Participants with HIV infection * Age \>= 18 years * All participants should have at least five (5) measurable cutaneous KS lesions with no previous local radiation, surgical or intralesional cytotoxic therapy that would prevent response assessment for that lesion. * Participants with stage T1 KS with visceral involvement must: * have any/all associated tumor associated symptoms \<= Grade 2 by Common Terminology Criteria for Adverse Events (CTCAE) v.6.0 criteria and/or, * require no immediate intervention (e.g., mild oozing of oral KS is allowed). * Participants did not receive prior systemic therapy for KS or received prior systemic therapy and currently are either plateau in response, relapsed disease, progressive disease (PD), or inadequate response to treatment. Note: Previous local therapy or radiation is not considered systemic therapy. * Participants must: * have been on effective ART therapy for at least 2 months prior to the study drug initiation and * have HIV VL \<= 100 copies/mL and * have persistent KS, affecting quality of life due to either T1 or T0 disease with inadequate disease regression on ART alone. * ECOG PS \<=3 * Adequate organ and marrow function as defined below: * absolute neutrophil count (ANC) \>= 500/mcL * platelets \>= 50,000/mcL * hemoglobin (hgb) \>= 8g/dL * total bilirubin \<= 1.5 institutional upper limit of normal (iULN) or \<3 x iULN for Gilbert s syndrome or HIV protease inhibitors * AST \<= 2.5 x iULN * ALT \<= 2.5 x iULN * CD4 T-cell count \<= 350/mcL * Participants must be willing to co-enroll to protocol 17C0174 "Molecular Characterization of Viral-associated Tumors, Tumors occurring in the Setting of HIV or other Immune Disorders and Castleman Disease" * Participants with chronic hepatitis B virus (HBV) infection are eligible if they are on suppressive antiviral therapy. * Participants with a hepatitis C virus (HCV) infection must have an undetectable HCV VL due to prior treatment or natural resolution. * Women of child-bearing potential (WOCBP) and men able to father a child must agree to use an effective method of contraception (hormonal, barrier, surgical sterilization, abstinence) at the study entry, for the duration of study therapy, and for up to 4 months after discontinuation of study drug. * Nursing participants must be willing to discontinue nursing from study treatment initiation through 4 months after the last dose of the study drug. * Participants must be able to understand and willing to sign a written informed consent document. EXCLUSION CRITERIA: -Participants who have not recovered from immune-related AEs due to prior therapy (i.e., have residual toxicities \> Grade 1 per CTCAE v.6.0). Note: Participants with hypothyroidism managed by supplemental levothyroxine are eligible. * History of severe allergic, anaphylactic, or other hypersensitivity reactions to Chinese Hamster Ovary (CHO) cell products, chimeric or humanized antibodies or fusion proteins. * Participants must not have received chemotherapy, radiotherapy, or other KS directed therapy other than ART for HIV within 2 weeks before the initiation of study drug. * Participants must not have received treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-TNF agents) or systemic immunostimulatory agents (including, but not limited to, interferon \[IFN\]-alpha or IL-2, pomalidomide, or immune checkpoint inhibitors) within 2 weeks before initiation of study treatment. Note: Participants who have received acute, low dose of systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled. The use of inhaled corticosteroids, and mineralocorticoids (e.g., fludrocortisone) for participants with orthostatic hypotension or adrenocortical insufficiency is allowed. * History or risk of autoimmune disease, except for: * the presence of laboratory evidence of autoimmune disease (e.g., history of positive antinuclear antibody \[ANA\] titer or lupus anticoagulant) without associated symptoms, * clinical evidence of vitiligo or other forms of depigmenting illness; and/or, * mild autoimmunity not impacting the function of major organs (e.g., limited psoriasis). * History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (e.g., bronchiolitis obliterans, cryptogenic organizing pneumonia), or evidence of active pneumonitis on screening chest x-ray. Note: History of radiation pneumonitis in the radiation field (fibrosis) is permitted. * History of allogeneic stem cell transplant and all other organ transplant. * Another prior or concurrent malignancy requiring active therapy * Active tuberculosis * Positive serum or urine beta-human chorionic gonadotropin (beta-hCG) test at screening. * Participants must not have received prohibited therapies within 4 weeks before initiation of study treatment * Severe uncontrolled intercurrent illness that would limit compliance with study requirements, as evaluated by history, physical exam, and chemistry panel.