A Study of sEphB4-HSA in Kaposi Sarcoma

Inclusion Criteria: * Participants may be treatment naïve, refractory to, or intolerant of one or more prior therapies, or treated with prior systemic treatment including but not limited to liposomal doxorubicin. * Participants must have biopsy-proven KS involving skin, with or without visceral involvement. * If HIV-positive, any CD4 count will be allowed on study. * Age ≥ 18 years. * ECOG performance status ≤ 2 or Karnofsky performance score (KPS) ≥ 50% * Life expectancy of greater than 3 months. * Absolute neutrophil count ≥ 1,000/mcL * Platelets ≥ 75,000/mcL * Total bilirubin ≤ 1.5 X ULN * AST (SGOT) / ALT (SGPT) ≤ 2.5 X ULN * Creatinine within normal institutional limit for the reference lab OR creatinine clearance ≥ 60 mL/min/1.73 m2 as calculated by Cockcroft-Gault formula for participants with creatinine levels above institutional normal. * Participants taking part in the optional biopsies must have cutaneous lesion(s) amenable to two (2) 5-mm tumor biopsy at study entry and optional second biopsy on therapy at week 8-12. Patients must have at least five additional lesions measurable for assessment with no improvement over the past month. * Females of childbearing potential (FCBP)† must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 14 days prior to enrollment and again within 24 hours prior to starting Cycle 1 of sEphB4-HSA. Further, they must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control: one highly effective method and one additional effective method AT THE SAME TIME during receipt of sEphB4-HSA, and 12 weeks after discontinuation of sEphB4-HSA. FCBP must also agree to ongoing pregnancy testing. Men must agree to use a latex condom during sexual contact with a FCBP even if they have had a successful vasectomy. * A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). * Documentation of HIV status. If participant is HIV positive, HIV-1 infection, as documented by any federally approved, licensed HIV rapid test performed in conjunction with screening (or ELISA test kit, and confirmed by Western blot or other approved test, or HIV rapid multispot antibody differentiation assay). Alternatively, this documentation may include a record demonstrating that another physician has documented the participant's HIV status based on either: 1) approved diagnostic tests, or 2) the referring physician's written record that HIV infection was documented, with supporting information on the participant's relevant medical history and/or current management of HIV infection. * If the participant is HIV negative, documentation of a negative result for any federally approved, licensed HIV rapid test within 4 weeks prior to study enrollment will suffice. If the initial rapid test is positive, further approved confirmatory test results must be present to document the subject's HIV status. * If participant is HIV positive, participant must be on a stable antiretroviral regimen for at least 12 weeks prior to study enrollment. * There should be no evidence for improvement in Kaposi Sarcoma in the 3 months prior to study enrollment, unless there is evidence for progression of Kaposi Sarcoma in the 4 weeks immediately prior to study enrollment. * Participants must, in the opinion of the investigator, be capable of complying with the protocol. Exclusion Criteria: * Inability to understand and inability to provide informed consent. * Participants who are receiving any other investigational agents. * Participants who have had anti-neoplastic treatment for KS (including chemotherapy, radiotherapy, local treatment including topical 5-FU, biological therapy or investigational therapy) within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study OR those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. * Participants with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to sEphB4-HSA or other agents used in study. * Concurrent, acute, active infection, or treatment for infection, other than oral thrush or genital herpes, within 14 days of enrollment. Mycobacterium avium complex (MAC) that is undergoing treatment is allowed. * Participants for whom front-line cytotoxic therapy is indicated (i.e. symptomatic visceral or pulmonary Kaposi Sarcoma or symptomatic Kaposi Sarcoma impairing functional status). * Concurrent neoplasia requiring cytotoxic therapy. * Participant is ≤ 2 years free of another primary malignancy. Exceptions include the following: * Basal cell skin cancer * Cervical carcinoma in situ * Anal carcinoma in situ * Any steroid treatment except for that required for replacement therapy in adrenal insufficiency, topical or injected testosterone for hypogonadism, or inhaled steroids for the treatment of asthma. * Previous local therapy of any KS-indicator lesion unless the lesion has clearly progressed since that local treatment. Any prior local treatment to indicator lesions regardless of the elapsed time should not be allowed unless there is evidence of clear-cut progression of said lesion. * Female participants who are pregnant, lactating, or breast-feeding. * Pregnant women are excluded from this study because sEphB4-HSA has not been tested in pregnant women and it could have potential teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with sEphB4-HSA, breastfeeding should be discontinued if the mother is treated with sEphB4-HSA. * Participants with a recent history (\< 6 months) of a major infarct including but not inclusive to bowel ischemia, cerebral vascular accident, transient ischemic attack, myocardial infarction, limb ischemia, or skin necrosis. * Participants with a QTcF (Fridericia Correction Formula) \> 480 ms on 2 out of 3 EKGs (if first EKG is \< 480, no need to repeat, if first EKG is \> 480 repeat twice for a total of 3 EKGs). * Participants with systolic blood pressure \>120 mm Hg or diastolic blood pressure \>80 mm Hg who are unwilling to start antihypertensives (see Section 5.4 uncontrolled sustained for recommendations for management of hypertension which will be defined as during the study), or participants with systolic blood pressure \> 140, and mm Hg, or diastolic blood pressure \> 90, even mm Hg, with or without use of anti-hypertensive medications. (participants may not enroll onto the study until BP is ≤ 140/90 mm Hg with or without antihypertensives). * Participants with a recent history (\< 6 months) of a major bleed which will be defined as a symptomatic bleeding in a critical area or organ, such as intracranial, intraspinal, intraocular, retroperitoneal, intraarticular or pericardial, or intramuscular with compartment syndrome, and/or bleeding causing a fall in hemoglobin level 2 grams/dL or more, or leading to transfusion of two or more units of whole blood or packed red cells. * Participants on any dose of warfarin or are on full dose anticoagulation with other agents including low molecular weight heparin, antithrombin agents, antiplatelet agents and full dose aspirin within 7 days prior to study enrollment; participants on prophylactic doses of low molecular weight heparin are allowed. * Cardiac related illnesses including, but not limited to: * Symptomatic congestive heart failure including participants with Grade III/IV cardiac disease as defined by the New York Heart Association functional criteria * Unstable angina pectoris * Cardiac arrhythmia * Physical or psychiatric illness/social situations that in the estimation of the investigator would limit compliance with study requirements or place the participant at high risk of toxicity or non-compliance. * Patients with a history of CVA or TIA in the past 12 months