Cabazitaxel, Carboplatin, and Cetrelimab Followed by Niraparib With or Without Cetrelimab for the Treatment of Aggressive Variant Metastatic Prostate Cancer

Inclusion Criteria

• •Completion of informed consent prior to any study specific procedures
• •Patients must agree to tissue collection for correlative studies at the specified timepoints
• •Patients must consent to the MD Anderson Immunotherapy Platform laboratory protocol PA13-0291
• •Histologically or cytologically confirmed prostate carcinoma
• •Presence of metastatic disease documented on imaging studies (bone scan, computed tomography \[CT\] and/or magnetic resonance imaging \[MRI\] scans)
• •Patients must meet at least one of the following AVPC criteria:
• •* Histologically proven small cell (neuroendocrine) prostate carcinoma
• •* Exclusive visceral metastases
• •* Predominantly lytic bone metastases identified by plain x-ray or CT scan
• •* Bulky (\>= 5 cm in longest dimension) lymphadenopathy or high-grade tumor mass in prostate/pelvis
• •* Low PSA (=\< 10 ng/mL) at initial presentation (prior to androgen ablation or at symptomatic progression in the castrate-setting) plus high volume (\>= 20) bone metastases
• •* Elevated serum lactate dehydrogenase (LDH) (\>= 2 x ULN) or elevated serum carcinoembryonic antigen (CEA) (\>= 2 x ULN) in the absence of other etiologies
• •* Short interval (=\< 180 days) to castrate-resistant progression following initiation of hormonal therapy
• •* Known loss or mutation (by Clinical Laboratory Improvement Act \[CLIA\] certified molecular testing, immunohistochemistry \[IHC\] and/or deoxyribonucleic acid \[DNA\] sequencing) in at least 2 of Tp53, RB1 and PTEN defined as:
• •* AVPC determination by immunohistochemistry. As previously described, tumor samples are considered negative (and thus abnormal) for RB1 and PTEN if their labeling index is =\< 10% and positive (and thus aberrant) for Tp53 if their labeling index is \>= 10%, where the labeling index is defined as the percentage of positive cells, and calculated as the number of positively stained epithelial cells divided by the total number of epithelial cells, at X200 magnification
• •* AVPC determination by DNA sequencing. As previously described, the TP53, RB1 and PTEN genes will be considered aberrant if they contain exonic nonsynonymous missense or stop-gain mutations, frameshift or non frameshift indels (insertions or deletions), and/or copy number losses
• •* Patients who have castration -resistant disease progression per RECIST in the absence of PSA values rising to ≥ 1.0ng/ml as per PCWG3 PSA progression criteria
• •Patients must have documented evidence of progressive disease as defined by any of the following: a) PSA progression: minimum of 2 rising values (3 measurements) obtained a minimum of 7 days apart with the last result being at least \>= 1.0 ng/mL; b) New or increasing non-bone disease (RECIST); c) Positive bone scan with 2 or more new lesions (Prostate Cancer Working Group 3 \[PCWG3\]); d) Increasing symptoms unequivocally attributed to disease progression as judged by the treating physician and the principal investigator (PI)
• •Surgically or ongoing medically castrated, with baseline testosterone levels of =\< 50 ng/dL (=\< 2.0 nM)
• •Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2
• •Hemoglobin \>= 10.0 g/dL (unless due to bone marrow infiltration by tumor, in which case hemoglobin \> 8 g/dL is allowed) (within 7 days prior to treatment registration). Patient may have blood transfusions prior to study enrollment
• •Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (unless due to bone marrow infiltration by tumor, in which case ANC \> 1,000/mm\^3 is allowed) (within 7 days prior to treatment registration)
• •White blood cells (WBC) \> 3 x 10\^9/L (unless due to bone marrow infiltration by tumor, in which case WBC \> 2 x 10\^9/L is allowed) (within 7 days prior to treatment registration)
• •No features suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) on peripheral blood smear (within 7 days prior to treatment registration)
• •Platelet count \>= 100 x 10\^9/L (unless due to bone marrow infiltration by tumor, in which case platelet \> 50,000/mm\^3 is allowed) (within 7 days prior to treatment registration)
• •Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (except for patients with known Gilbert's disease) (within 7 days prior to treatment registration)
• •Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal (unless liver metastases are present in which case it must be =\< 5 x ULN) (within 7 days prior to treatment registration)
• •Calculated creatinine clearance (Cockcroft-Gault equation) \>= 30 mL/min (within 7 days prior to treatment registration)
• •Able to swallow study drugs whole as a tablet/capsule
• •Patients who have partners of childbearing potential (e.g. female that has not been surgically sterilized or who are not amenorrheic for \>= 12 months) must be willing to use a method of birth control in addition to adequate barrier protection as determined to be acceptable by the investigator during the study and for 3 months after last dose of niraparib administration and 5 months after the last dose of cetrelimab. In addition men should not donate sperm during this period. Please note that the efficacy of hormonal contraception may be decreased if administered with niraparib
• •Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up