• Subject must be 18 years of age or older at the time the Informed Consent is signed.

• The subject (or legally acceptable representative if applicable) must provide written informed consent for the trial.

• Pathologic diagnosis of prostate cancer of adenocarcinoma or small cell histology.

• Metastatic disease as documented by technetium-99m (99mTc) bone scan or metastatic lesions by computed tomography (CT) or magnetic resonance imaging (MRI) scans (visceral or lymph node disease). CT-portion of FDG-PET/CT or scan may be used for eligibility. NaF PET-CT is an alternative to 99mTc bone scan. If lymph node metastasis is the only evidence of metastatic disease, it must be 1.5 cm in short axis and above the level of the iliac bifurcation. Imaging studies for the purpose of determining eligibility must be completed within 60 days of Day 1.

• Progressive castration resistant prostate cancer as defined by serum testosterone \< 50 ng/mL and one of the following:

‣ PSA progression confirmed per Prostate Cancer Clinical Trials Working Group (PCWG3),

⁃ Radiographic progression of soft tissues according to Response Evaluation Criteria in Solid Tumors, version 1.1 (iRECIST 1.1) modified based on PCWG3, or radiographic progression of bone according to PCWG3.

• Prior use of a novel AR signaling inhibitor for 4 weeks, including abiraterone acetate plus prednisone/prednisolone, enzalutamide, apalutamide, and/or darolutamide.

∙ NOTE: These AR signaling inhibitors may have been used for mCSPC, M0CRPC, and/or mCRPC.

• Ongoing surgical or medical castration, with testosterone levels of \<50 ng/dL. If the subject is being treated with GnRH analogs (subject who has not undergone bilateral orchiectomy), this therapy must have been initiated at least 30 weeks prior to initiation of pembrolizumab and must be continued throughout the study.

• ECOG PS grade of 0-1.

• Metastatic lesion that is amenable to biopsy and performed within 180 days of Day 1.

• dMMR or CDK12-/- as determined by somatic tumor DNA NGS.

‣ Either monoallelic or biallelic inactivation of CDK12 on NGS is considered sufficient for eligibility purposes.

⁃ MMR genes include: MLH1, MSH2, MLH3, PMS1, MSH6, and PMS2.

⁃ dMMR is established by MSI-H on NGS. However, for weak MMR genes, inclusive of PMS2 and MSH6, monoallelic inactivation will be allowed for eligibility purposes if and only if there is at least MSI-low or hypermutation that is concomitantly present.

⁃ If there is biallelic inactivation of strong MMR genes (MLH1 and MSH2), then patients must manifest MSI-H. However, if the tumor DNA utilized for MSI analysis was obtained \> 6 months prior to NGS, then the NGS should be repeated to determine if MSI-H has developed. Monoallelic inactivation of strong MMR genes will be allowed if MSI-H is present; in this scenario, it is presumed that biallelic inactivation is present but the second inactivating event was not detected due to technical issues such as low sensitivity for copy loss.

• Adequate organ function:

‣ Hemoglobin (hgb) \> 9.0 g/dL,

⁃ Absolute neutrophil count (ANC) \> 1500/ uL,

⁃ Platelets \> 100,000/ uL,

⁃ Total bilirubin 1.5 x ULN OR direct bilirubin ULN for participants with total bilirubin levels \>1.5 x ULN

⁃ ALT and AST 2.5 x ULN ( 5 x ULN for participants with liver metastases) (Child-Pugh class A and B allowed; Child-Pugh class C is excluded).

⁃ Creatinine \< (2.0 mg/dL) during screening evaluation (\>2.0 is allowed if EGFR \>30 mL/min/1.73 m2).

• Subject must agree to use contraception during the treatment period plus an additional 120 days after the last dose of study treatment and must refrain from donating sperm during this period.