Docetaxel, Carboplatin, and Rucaparib Camsylate in Treating Patients With Metastatic Castration Resistant Prostate Cancer With Homologous Recombination DNA Repair Deficiency

This phase II trial studies how well docetaxel with carboplatin followed by rucaparib camsylate works in treating patients with metastatic castration resistant prostate cancer (spread outside of prostate and resistant to testosterone suppression) with homologous recombination DNA repair deficiency. Chemotherapy drugs, such as docetaxel and carboplatin, work to stop the growth of cancer cells, by stopping them from dividing or spreading. Rucaparib camsylate may stop the growth of tumor cells with defects in the ability to repair mistakes in DNA by forcing additional errors so that the cancer cells cannot overcome the number of errors and will then die. Giving induction docetaxel and carboplatin followed by maintenance rucaparib camsylate may work better in treating patients with castration resistant prostate cancer.

OUTLINE:

INDUCTION: Patients receive docetaxel intravenously (IV) and carboplatin IV on day 1. Treatment repeats every 21 days for 4 cycles in the absence of disease progression or unacceptable toxicity.

MAINTENANCE: Patients receive rucaparib camsylate orally (PO) twice daily (BID) on days 1-28. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up periodically.

Eligibility Criteria:
Inclusion Criteria:

* Signed informed consent form (ICF) providing agreement to adhere to the dosing schedule, report for all trial visits and authorization, use and release of health and research trial information
* Histologically or cytologically confirmed adenocarcinoma of the prostate (excluding predominant small cell histology)
* Ongoing gonadal androgen deprivation therapy with gonadotropin-releasing hormone (GnRH) analogues, antagonists or orchiectomy; patients who have not had an orchiectomy must be maintained on effective GnRH analogue/antagonist therapy
* Castration resistant prostate cancer as defined by serum testosterone \< 50 ng/ml and PSA level of at least 2 ng/ml that has risen on at least 2 successive occasions at least 1 week apart
* Presence of metastatic disease on bone or computed tomography (CT) scan

  * Evaluable disease progression by modified RECIST 1.1 (Response Evaluation Criteria in Solid Tumors)
  * Bone disease on bone scan
* Prior therapy with sipuleucel-T, abiraterone, enzalutamide, docetaxel, and/or cabazitaxel; there is no limit to the number of prior treatment regimens in the castration resistant setting, so long as prior therapy does not include platinum chemotherapy or a PARP inhibitor; prior platinum chemotherapy in the hormone sensitive setting is permitted, so long as it has been at least 6 months since last dose
* Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1
* Life expectancy \>= 12 weeks
* No prior malignancy is allowed except:

  * Adequately treated basal cell or squamous cell skin cancer or
  * In situ carcinoma of any site or
  * Other adequately treated malignancy for which the patient has been disease-free for at least one year (any prior chemotherapy is allowed)
* Documented evidence of at least ONE or MORE of the following:

  \* Pathogenic mutation or inactivating alteration of a gene involved in homologous recombination repair in the tumor
  * Note, that if this alteration is identified in a circulating tumor deoxyribonucleic acid (ctDNA) assay, the variant-allele fraction must be \> 20% to indicate relevance to predominant tumor clone

    * Mutation in one or more other genes involved in homologous DNA recombination repair in the tumor may be included at investigator's discretion
    * Homologous recombination repair deficiency by genomic signature in the tumor by BROCA-HR, Foundation One or equivalent assay
    * Presence of pathogenic or likely pathogenic germline mutation/variant in BRCA2, BRCA1, ATM or PALB2
  * Note: Germline mutations in other HR genes will be considered at investigator's discretion)
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (within 14 days of first dose of study drug)
* Platelets \> 100 x 10\^9/L (within 14 days of first dose of study drug)
* Hemoglobin \>= 9 g/dL (within 14 days of first dose of study drug)
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x ULN; if liver metastases, then =\< 5 x ULN (within 14 days of first dose of study drug)
* Bilirubin =\< 1.5 x ULN (\< 2 x ULN if hyperbilirubinemia is due to Gilbert's syndrome) (within 14 days of first dose of study drug)
* Serum creatinine =\< 1.5 x ULN or estimated glomerular filtration rate (GFR) \>= 45 mL/min using the Cockcroft Gault formula (within 14 days of first dose of study drug)

Exclusion Criteria:

* Currently receiving active therapy for other neoplastic disorders
* Symptomatic and/or untreated central nervous system (CNS) metastases; patients with asymptomatic previously treated CNS metastases are eligible provided they have been clinically stable for at least 4 weeks
* Known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness, active or symptomatic viral hepatitis or chronic liver disease
* Clinically significant heart disease as evidenced by myocardial infarction, or arterial thrombotic events in the past 6 months, severe or unstable angina, or New York Heart Association (NYHA) class II-IV heart disease or cardiac ejection fraction measurement of \< 35 % at baseline
* Treatment with an investigational therapeutic drug within 30 days of cycle 1
* Prior therapy with a PARP inhibitor (e.g., olaparib, talazoparib, veliparib, niraparib, rucaparib)
* Prior therapy with a platinum chemotherapy (e.g. cisplatin, carboplatin, oxaliplatin) in the castration resistant setting; (prior platinum chemotherapy in the hormone sensitive setting is permitted, so long as time since last dose is 6 months or greater)
* Active, ongoing toxicity (Common Terminology Criteria for Adverse Events \[CTCAE\] grade 2 or higher) from prior therapy
* Presence of dementia, psychiatric illness, and/or social situations limiting compliance with study requirements or understanding and/or giving of informed consent
* Pre-existing duodenal stent and/ or any gastrointestinal disorder or defect that would, in the opinion of the Investigator, interfere with absorption of rucaparib
* Any condition(s), medical or otherwise, which, in the opinion of the investigators, would jeopardize either the patient or the integrity of the data obtained