Inclusion Criteria:

          -  Patients must have histologically confirmed Kaposi sarcoma

          -  Patients must have evaluable disease. Note: Kaposi sarcoma will be evaluated using a
             modified version (consistent with National Cancer Institute [NCI] studies) of the
             Acquired Immunodeficiency Syndrome (AIDS) Clinical Trial Group (ACTG) Oncology
             Committee staging and response definitions for KS

          -  No upper or lower limit on the number of prior therapies or stage of disease

          -  HIV-positive patients must have been on effective anti-retroviral (ART) therapy for at
             least 3 months prior to enrollment, with persistent KS affecting quality of life due
             to either T1 disease or T0 disease with inadequate disease regression on ART alone

          -  HIV-positive patients must have undetectable HIV viral loads =< 40 copies/mL measured
             using a Food and Drug Administration (FDA)-approved commercial assay with lower limit
             of detection between =< 20 copies/mL and =< 40 copies/mL

          -  Patients with visceral involvement must:

               -  Meet other eligibility criteria

               -  Have any/all associated tumor associated symptoms =< grade 2 by Common
                  Terminology Criteria for Adverse Events (CTCAE) criteria; and/or

               -  Require no immediate intervention (e.g. mild oozing of oral KS not an exclusion
                  criteria)

          -  Patients must provide newly obtained core, punch, or excisional biopsy of a tumor
             lesion obtained up to 28 days prior to treatment initiation. An archival tumor sample
             obtained within 1 year of screening is allowed if pre treatment biopsy is deemed
             unsafe or technically not feasible

          -  Patients must be >= 18 years of age on day of signing informed consent document.
             Because no dosing or adverse event data are currently available on the use of NT-I7 in
             patients < 18 years of age, children are excluded from this study but will be eligible
             for future pediatric trials

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)

          -  Leukocytes >= 2,500/mcL

          -  Absolute neutrophil count >= 1,000/mcL

          -  Platelets >= 100,000/mcL

          -  Hemoglobin >= 9/dL

          -  Total bilirubin =< 1.5 institutional upper limit of normal (ULN) OR < 3 x
             institutional ULN for Gilbert's syndrome or HIV protease inhibitors

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) /
             alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase [SGPT]) =< 2.5 x
             institutional ULN

          -  Creatinine =< 2 x institutional ULN OR creatinine clearance >= 60 mL/min/1.73 m^2 by
             Cockcroft-Gault. At the discretion of the treating physician, a 24-hour urine
             creatinine clearance could be obtained and utilized as the gold standard if creatinine
             clearance by Cockcroft-Gault is < 30 and prevents patient enrollment on the trial

          -  Patients with chronic hepatitis B virus (HBV) infection must be on suppressive
             antiviral therapy

          -  Patients with a history of hepatitis C virus (HCV) infection must have an undetectable
             HCV viral load due to prior treatment or natural resolution

          -  Female patients of childbearing potential must have a negative urine or serum
             pregnancy test within 72 hours before receiving the first dose of the study agent. If
             the urine test is positive or cannot be confirmed as negative, a serum pregnancy test
             will be required

          -  The effects of NT-I7 on the developing human fetus are unknown. For this reason and
             because NT-I7 may have an adverse effect on pregnancy and poses risk to the human
             fetus, women of child-bearing potential and men must agree to use adequate
             contraception (hormonal or barrier method of birth control; abstinence) prior to study
             entry, for the duration of study participation, and for 90 days after the last dose of
             study treatment. Should a woman become pregnant or suspect she is pregnant while she
             or her partner is participating in this study, she should inform her treating
             physician immediately. Men treated or enrolled on this protocol must also agree to use
             adequate contraception prior to the study, for the duration of study participation,
             and for 90 days after completion of NT-I7 administration

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  Patients who have had chemotherapy, radiotherapy or other KS directed therapy other
             than ART for HIV within 2 weeks before the initiation of study treatment

          -  Patients who have not recovered from immune related adverse events due to prior
             therapy (i.e., have residual toxicities > grade 1) with the exception of
             hypothyroidism managed by supplemental levothyroxine

          -  Patients who have received treatment with any other investigational agent within 4
             weeks before initiation of study treatment

          -  Patients with known hypersensitivity to Chinese hamster ovary cell products or other
             recombinant human antibodies

          -  Patients who have a history of severe allergic, anaphylactic, or other
             hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins

          -  Patients who have received treatment with systemic immunostimulatory agents
             (including, but not limited to, interferon [IFN]-alpha or interleukin [IL]-2,
             pomalidomide, or immune checkpoint inhibitors) within 6 weeks before initiation of
             study treatment

          -  Patients who have received treatment with systemic immunosuppressive medications
             (including, but not limited to, prednisone, cyclophosphamide, azathioprine,
             methotrexate, thalidomide, and antitumor necrosis factor [anti-TNF] agents) within 2
             weeks before initiation of study treatment

               -  Patients who have received acute, low dose, 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 patients with orthostatic hypotension or adrenocortical
                  insufficiency is allowed

          -  Patients who have a history or risk of autoimmune disease, including, but not limited
             to, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease,
             vascular thrombosis associated with antiphospholipid syndrome, Wegener's
             granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple
             sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis. Note: the
             following will NOT be exclusionary:

               -  The presence of laboratory evidence of autoimmune disease (e.g., positive
                  antinuclear antibody (ANA) titer or lupus anticoagulant) without associated
                  symptoms

               -  Clinical evidence of vitiligo or other forms of depigmenting illness

               -  Mild autoimmunity not impacting the function of major organs (e.g., limited
                  psoriasis)

          -  Patients with uncontrolled intercurrent illness including, but not limited to,
             symptomatic congestive heart failure (New York Heart Association Class III or IV),
             unstable angina pectoris, cardiac arrhythmia, recent myocardial infarction (within the
             last 6 months). Patients with known history of treatment with cardiotoxic agents,
             including anthracyclines, should have a clinical risk assessment of cardiac function
             using the New York Heart Association Functional Classification

          -  Psychiatric illness/social situations that would limit compliance with study
             requirements

          -  Pregnant women are excluded from this study because the effects of NT-I7 on the
             developing human fetus are unknown. Because there is an unknown but potential risk for
             adverse events in nursing infants secondary to treatment of the mother with NT-I7,
             breastfeeding should be discontinued if the mother is treated with NT-I7

          -  Patients with a history of solid organ or allogeneic stem cell transplant

          -  Patients with continuing KS regression on ART alone. Stable disease allowed

          -  Patients with a prior or concurrent malignancy requiring active therapy

          -  Patients with active tuberculosis

          -  Patients who have a history of idiopathic pulmonary fibrosis, pneumonitis (including
             drug induced), organizing pneumonia (bronchiolitis obliterans, cryptogenic organizing
             pneumonia, etc.), or evidence of active pneumonitis on screening chest computed
             tomography (CT) scan. History of radiation pneumonitis in the radiation field
             (fibrosis) is permitted