Standard Chemotherapy and Donor Bone Marrow Transplant after Chemotherapy in Treating Patients with Metastatic Castration-Resistant Prostate Cancer

Inclusion Criteria

• Performance status =< 1
• Histologically-confirmed adenocarcinoma of the prostate
• Treated with continuous androgen ablative therapy (either surgical castration or gonadotrophin releasing hormone [LHRH] agonist/antagonist) with documented castrate level of serum testosterone (< 50 ng/dl)
• Metastatic disease radiographically documented by CT or bone scan
• Patient must be HLA typed at high resolution using deoxyribonucleic acid (DNA) based typing at the following loci: HLA-A, -B, -C, and DRB1
• Patient must have available one or more potential first (biologic mother, sister, half-sister, or daughter) or second-degree related female donor; mothers and daughters have a 100% chance of being haploidentical matches, sisters a 75% chance of being matched or haploidentical, and second degree relatives have a 50% chance of being haploidentical matches; the donor and recipient must be HLA identical for at least one antigen at HLA-A, -B, -C and HLA-DRB1
• Screening PSA must be >= 1.0 ng/mL
• Prior therapy with second line hormonal therapy is allowed (i.e. bicalutamide, nilutamide, flutamide, ketoconazole, abiraterone, enzalutamide, ARN-509)
• Prior docetaxel as first line therapy in addition to androgen deprivation is allowed
• Cardiac ejection fraction at rest must be >= 40%
• Bilirubin < 2.5 mg/dL (unless due to Gilbert's disease)
• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) < 5 times upper limit of normal (ULN)
• Serum creatinine within normal range
• Carbon monoxide diffusing capability (DLCO) (corrected for hemoglobin), forced expiratory volume in 1 second (FEV1) and forced vital capacity (FVC) > 50% predicted
• At least 4 weeks (wks) since prior radiation or surgery with full recovery (no persistent toxicity >= grade 1)
• Ability to understand and willingness to sign a written informed consent document

Exclusion Criteria

• Prior treatment with chemotherapy (docetaxel or cabazitaxel) for castration resistant prostate cancer
• Evidence of serious and/or unstable pre-existing medical, psychiatric or other condition (including laboratory abnormalities) that could interfere with patient safety or provision of informed consent to participate in this study
• Active uncontrolled infection, including known history of human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) or hepatitis B or C
• Any psychological, familial, sociological, or geographical condition that could potentially interfere with compliance with the study protocol and follow-up schedule