Docetaxel and Carboplatin in Treating Patients With Metastatic, Castration Resistant Prostate Cancer Containing Inactivated Genes in the BRCA 1/2 Pathway

This pilot clinical trial studies docetaxel and carboplatin in treating patients with castration resistant prostate cancer that has spread from the primary site (place where it started) to other places in the body (metastatic) and contains inactivated genes in the BRCA 1/2 pathway. Drugs used in chemotherapy, such as docetaxel and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading.

OUTLINE:

Patients receive docetaxel intravenously (IV) over 30-60 minutes and carboplatin IV over 30-60 minutes on day 1. Treatment repeats every 21 days for 10 courses in the absence of disease progression or unacceptable toxicity.

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 carcinoma of the prostate (excluding neuroendocrine differentiation or squamous 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 rising PSA when serum testosterone \< 50 ng/ml (note: current testosterone results are not required if the potential subject has not missed any GnRH analogue/antagonist doses since their last result was received) AND one of the following:

  * PSA level of at least 2 ng/ml that has risen on at least 2 successive occasions at least 1 week apart
  * Evaluable disease progression by modified RECIST (Response Evaluation Criteria in Solid Tumors)
  * Progression of metastatic bone disease on bone scan with \> 2 new lesions
* Prior therapy with abiraterone, enzalutamide and/or docetaxel; there is no limit to the number of prior treatment regimens
* Presence of metastatic disease on scans
* 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)
* Absolute neutrophil count \>= 1.5 x 10\^9 cells/L
* Hemoglobin (Hgb) \>= 9.0 g/dL
* Platelets \>= 100,000 x 10\^9/L
* Aspartate aminotransferase (AST), alanine aminotransferase (ALT) =\< 1.5 x upper limit of normal (ULN)
* Total bilirubin levels =\< 1.5 x ULN
* Patients must have clear and documented evidence of biallelic inactivation BRCA1, BRCA2 or ATM by sequencing, for example University of Washington (UW)-Oncoplex, SU2C, or Foundation One testing and/or patients with clearly deleterious mutations of other genes involved in homologous DNA repair (e.g., partner and localizer of BRCA2 \[PALB2\], BRCA1-interacting protein 1 \[BRIP1\], etc.) by sequencing via UW-Oncoplex, SU2C, or Foundation One testing may be included at the investigator's discretion

Exclusion Criteria:

* Currently receiving active therapy for other neoplastic disorders
* Histologic evidence of neuroendocrine or small cell carcinoma of the prostate
* Known parenchymal brain metastasis
* 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, if done
* Treatment with an investigational therapeutic within 30 days of cycle 1
* Patients with dementia/psychiatric illness/social situations limiting compliance with study requirements or understanding and/or giving of informed consent are not eligible
* Any medical conditions, which, in the opinion of the investigators, would jeopardize either the patient or the integrity of the data obtained are not eligible