IL-15 superagonist with or without a PSA vaccine in biochemically recurrent prostate cancer after SBRT

* INCLUSION CRITERIA:
* Histopathological confirmation of prostate adenocarcinoma by the Laboratory of Pathology at the National Institutes of Health (NIH) Clinical Center prior to the study treatment initiation. If no pathologic specimen is available, participants may enroll with a pathologist s report showing a histologic diagnosis of prostate adenocarcinoma and a clinical course consistent with the disease from any outside site.
* Biochemically recurrent prostate cancer, defined as PSA over 0.8 ng/ml following radical prostatectomy or \>= 2 ng/ml above the nadir following definitive radiotherapy or definitive radiotherapy (including brachytherapy) for localized prostate cancer.
* Participants must be at least 1 year removed from definitive local therapy before the study treatment initiation.
* Recovery to baseline from acute toxicity related to prior therapy, including surgery and radiation.
* Hepatic function eligibility parameters: Bilirubin (total and direct) \<= upper limit of normal (ULN) (OR in participants with Gilbert s syndrome, a total bilirubin \<= 3.0), aspartate transaminase (AST) and alanine transaminase (ALT) \<= 1.5 times upper limit of normal.
* Adequate renal function defined by a calculated creatinine clearance \> 50 mL/min according to the Cockcroft-Gault formula or by measure of creatinine clearance from 24-hour urine collection.
* ECOG performance score 0-1.
* No other active malignancies within the 36 months prior to the study treatment initiation (with the exception of nonmelanoma skin cancers or carcinoma in situ of the bladder).
* 18 years of age or older.
* Individuals must agree to use effective contraception (barrier, vasectomy and/or abstinence) for the duration of study therapy and for four months after the last treatment administration. Individuals with partners with birthing potential will be recommended that their partner use a highly effective contraception (includes use of oral, injected or implanted hormonal methods of contraception, placement of certain intrauterine devices (IUD) or intrauterine systems (IUS), hysterectomy, oophorectomy, salpingectomy.
* Individuals must agree to not donate sperm during the restricted period (for the duration of study therapy and for four months after the last dose of study treatment).
* Negative CT scan/ Magnetic resonance imaging (MRI) for evidence of soft tissue metastasis (visceral or lymph node).
* Negative Tc99 for evidence of bone disease.
* Participants must have had prior SBRT to PSMA+ findings beyond the prostate and have had a documented 25% or more PSA rise from post-SBRT nadir
* Baseline testosterone \>= 100 ng/dl.
* Hematological parameters:

  * Granulocyte count \>= 1000/mm\^3
  * Platelet count \>= 100000/mm\^3
  * Hemoglobin (Hgb) \>= 10 g/dL
* Participants must be able to understand and willing to sign a written informed consent document.

EXCLUSION CRITERIA:

* Immunocompromised status due to:

  * Human immunodeficiency virus (HIV) seropositivity
  * HBV or HCV seropositivity
  * Other immunodeficiency diseases
* Active autoimmune diseases such as Addison's disease, Hashimoto's thyroiditis, systemic lupus erythematosus, Sjogren syndrome, scleroderma, myasthenia gravis, Goodpasture syndrome or active Grave's disease. Participants with a history of autoimmunity that has not required systemic immunosuppressive therapy or does not threaten vital organ function including central nervous system (CNS), heart, lungs, kidneys, skin, and gastrointestinal (GI) tract will be allowed. Participants with diabetes type I, vitiligo, or alopecia are allowed.
* Receipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant).
* Chronic administration (defined as daily or every other day for continued use \> 14 days) of systemic corticosteroids within 28 days before the study treatment initiation. Note: Use of corticosteroids with minimal systemic absorption (e.g., inhaled steroids, nasal sprays, and topical agents) is allowed.
* Other medications used for urinary symptoms including 5-alpha reductase inhibitors (finasteride and dutasteride) and alternative medications known to alter PSA (e.g., phytoestrogens and saw palmetto) within 28 days prior to the study treatment initiation.
* Major surgery within 28 days prior to study treatment initiation.
* Systemic therapy, including any investigational therapy within 28 days prior to the study treatment initiation.
* Radiation therapy within 14 days prior to the study treatment initiation.
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to the study drugs.
* Clinically significant cardiovascular/cerebrovascular disease as follows: cerebral vascular accident/stroke (\< 6 months prior to the first planned dose of study drugs), myocardial infarction (\< 6 months prior to the first planned dose of study drugs), or any of the following at time of enrollment: unstable angina, congestive heart failure (New York Heart Association Classification Class \>= II), serious cardiac arrhythmia, or uncontrolled hypertension (SBP\>170/ DBP\>105).
* Serious intercurrent medical illness evaluated by medical history and physical exam that would interfere with participant's ability to carry out the treatment program.