Inclusion Criteria:

          -  Patients must have a pathologically confirmed diagnosis of prostate adenocarcinoma

          -  Patients must have metastatic (M1) disease as evidenced by soft tissue and/or bony
             metastases on computed tomography (CT) or magnetic resonance imaging (MRI) scan or
             technetium bone scan

          -  Patients must have castration resistant disease with disease progression despite
             castrate levels of testosterone (testosterone =< 50 ng/dL)

          -  Patients must have received and progressed on at least one second generation androgen
             receptor (AR) targeted therapy for castration resistant disease irrespective of prior
             chemotherapy. No more than 3 prior treatment therapies for castration resistant
             disease (life prolonging) are permitted. Prior therapy can include:

               -  Second generation AR targeted therapy (i.e. abiraterone, enzalutamide, or other
                  new antiandrogen [ODM-201, apalutamide])

               -  Chemotherapy (docetaxel and/or cabazitaxel)

          -  Documented progressive mCRPC based on at least one of the following criteria:

               -  PSA progression defined as 25% increase over baseline value with an increase in
                  the absolute value of at least 2.0 ng/mL that is confirmed by another PSA level
                  with a minimum of a 1 week interval and a minimum PSA of 2.0 ng/mL

               -  Progression of bi-dimensionally measurable soft tissue or nodal metastasis
                  assessed within one month prior to registration by a CT scan or MRI

               -  Progression of bone disease (evaluable disease) (new bone lesion[s]) by bone scan

          -  Serum testosterone < 50 ng/dL. Patients must continue primary androgen deprivation
             therapy (ADT) with a luteinizing hormone-releasing hormone (LHRH) analogue (agonist or
             antagonist) if they have not undergone orchiectomy

          -  Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of
             0-2

          -  Patients must have adequate organ and bone marrow function as defined below within 28
             days of registration:

          -  Absolute neutrophil count >= 1,000/mcL (within 28 days of registration)

          -  Hemoglobin >= 9 g/dL* (within 28 days of registration)

               -  Transfusion is allowed as long as patients have not received prior transfusion =<
                  28 days from registration

          -  Bilirubin =< 1.5 x institutional upper limit of normal (ULN) except for unconjugated
             hyperbilirubinemia or Gilbert?s syndrome, who can have total bilirubin < 3.0 mg/dL
             (within 28 days of registration)

          -  Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 3 x ULN (=< 5 x ULN
             if liver metastases present) (within 28 days of registration)

          -  Serum creatinine =< 2.0 X ULN (upper limit of normal) or creatinine clearance >= 30
             mL/minute (using Cockcroft/Gault formula) (within 28 days of registration)

          -  Platelet >= 100,000 (within 28 days of registration)

          -  Patients must use a condom during treatment and for 3 months after the last dose of
             study treatment when having sexual intercourse. Female partners of male subjects
             should also use a highly effective form of contraception if they are of childbearing
             potential. Subjects should not donate sperm throughout the study and for 3 months
             following the last dose of treatment

          -  Patients must have the ability to understand and the willingness to sign a written
             informed consent prior to registration on study

        Exclusion Criteria:

          -  Patients who have received more than 3 prior treatment therapies (life prolonging) for
             mCRPC are not eligible

          -  Patients who have had radiotherapy =< 14 days prior to entering the study are not
             eligible

               -  Note: Palliative radiation therapy is allowed

          -  Patients who have had systemic therapy for prostate cancer =< 21 days or 5-half lives
             (whichever is shorter) are not eligible

               -  Note: Patients can receive a stable dose of bisphosphonates for bone metastases,
                  including zoledronic acid, or denosumab before and during the study as deemed
                  appropriate by the treating physician. Patients must continue androgen
                  deprivation therapy

          -  Patients receiving any other investigational agents are not eligible

          -  Patients with small cell carcinoma of the prostate are not eligible

               -  Note: Neuroendocrine differentiation is permitted. If there is doubt about this
                  and it is clinically indicated then a biopsy should be obtained to document
                  histological differentiation

          -  Patients who have a history of allergic reactions attributed to compounds of similar
             chemical or biologic composition to sEphB4-HSA are not eligible. AND patients who have
             had prior exposure to compounds of similar chemical or biologic composition to
             sEphB4-HSA are not eligible

          -  Patients who have an uncontrolled intercurrent illness including, but not limited to
             any of the following, are not eligible:

               -  Ongoing or active infection requiring systemic treatment

               -  Symptomatic congestive heart failure (New York Heart Association class III or IV
                  congestive heart failure)

               -  Unstable angina pectoris

               -  Serious cardiac arrhythmia

          -  Patients with uncontrolled hypertension (defined as systolic blood pressure [BP] >=
             160 mmHg or diastolic BP >= 95 mmHg) are not eligible

               -  Note: Patients with a history of hypertension are allowed provided blood pressure
                  is controlled by anti-hypertensive treatment

          -  Patients with electrocardiogram (ECG) with QT interval (corrected QT interval [QTc]) >
             480 msec are not eligible

          -  Patients with other malignancy that has progressed or has required active systemic
             treatment in the last 3 years

               -  Note: Patients with basal cell carcinoma of the skin, squamous cell carcinoma of
                  the skin that has undergone potentially curative therapy or carcinoma in situ or
                  non-muscle invasive bladder cancer are not excluded

          -  Patients with known active central nervous system (CNS) metastases and/or
             carcinomatous meningitis are not eligible

               -  Note: A scan to confirm the absence of brain metastases is not required. Subjects
                  with previously treated brain metastases may participate provided they are
                  stable, i.e. without evidence of progression for at least 4 weeks by repeat
                  imaging (note that the repeat imaging should be performed during study
                  screening), without requirement of steroid treatment for at least 4 weeks prior
                  to randomization and with any neurologic symptoms resolved or have returned to
                  baseline of prior treatment for brain metastasis

          -  Patients with spinal cord compression are not eligible unless considered to have
             received definitive treatment for this and evidence of stable disease for 28 days

          -  Patients who underwent major surgery =< 14 days of starting study treatment or have
             not recovered from effects of surgery are not eligible