Inclusion Criteria

          1. Age ≥ 18 years

          2. Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

          3. Life expectancy of at least 3 months

          4. Histologically confirmed prostate cancer. Treatment-emergent small cell/NEPC
             (neuroendocrine prostate cancer) is allowed, but de novo small cell carcinoma of the
             prostate is excluded.

          5. Progressive metastatic prostate cancer despite castrate levels of testosterone (< 50
             ng/dL).

          6. Patients may have either non-measurable disease OR measurable disease (by RECIST
             criteria)

          7. Progressive disease during treatment (or within 4 weeks of completion) with
             abiraterone, enzalutamide, and/or apalutamide based on any one of the following:

               -  For patients with measurable disease, progression by the RECIST 1.1 criteria

               -  PSA evidence for progressive prostate cancer consists of a PSA level of at least
                  2 ng/ml which has risen on at least 2 successive occasions, at least one week
                  apart. If the confirmatory PSA value is less than the screening PSA value, then
                  an additional test for rising PSA will be required to document progression for
                  the purposes of eligibility

               -  Radionuclide bone scan: At least two new foci consistent with metastatic lesions

          8. Testosterone < 50 ng/dL. Patients must continue primary androgen deprivation with an
             LHRH analogue if they have not undergone bilateral orchiectomy.

          9. Prior therapy with taxane in the castrate-sensitive or castration-resistant settings
             will be allowed. Prior treatment with radium-223 or sipuleucel-T is permitted, but not
             required.

         10. No other systemic therapies for prostate cancer within 21 days prior to cycle 1 day 1
             of study therapy or 5 half-lives, whichever is shorter, prior to day 1 of study
             therapy.

         11. Left ventricular ejection fraction (LVEF) ≥ 50% as determined by Multiple Gated
             acquisition (MUGA) scan or echocardiogram (ECHO) obtained during screening

         12. Patients must have adequate organ and bone marrow function within 14 days of inclusion
             in the study as defined below:

               -  Absolute Neutrophil Count ≥ 1,500/mm3

               -  Hemoglobin ≥ 9 g/dL

               -  Platelets ≥ 100,000 /mm3

               -  PT/INR ≤ 1.5 x ULN unless on chronic and stable anticoagulation at time of study
                  entry

               -  Bilirubin ≤1.5 x institutional upper limit of normal (ULN) except for
                  unconjugated hyperbilirubinemia or Gilbert's Syndrome, who can have total
                  bilirubin <3.0 mg/dL

               -  AST/ALT ≤ 3 x ULN (≤ 5 x ULN if liver metastases present)

               -  Lipase ≤ 1.5 x ULN

               -  HbA1c < 8.5 %

               -  Serum Creatinine ≤ 1.5 X ULN (upper limit of normal) or creatinine clearance ≥ 45
                  mL/minute (using Cockcroft/Gault formula)

         13. Sexually active males must use a condom with spermicide during intercourse while
             taking the drug and for 6 months after stopping treatment, even if patient is
             vasectomized to prevent delivery of the drug via seminal fluid.

         14. Patients must agree to provide tumor tissue, either fresh or archival specimen of
             primary tumor and/or metastatic lesion, if available. Availability of tissue will not
             be required for enrollment.

         15. Subjects must have the ability to understand and the willingness to sign a written
             informed consent prior to registration on study. Subjects should be willing and able
             to comply with the protocol for the duration of the study including undergoing
             treatment and scheduled visits and examinations at the institution.

         16. Only during phase 2, patients will be required to have mutations in DNA repair genes
             based on molecular tests performed on germline DNA, prostate cancer tissue or ctDNA.
             Qualifying mutations (i.e. deleterious/pathogenic alterations) in at least one of the
             following genes involved with homologous recombination repair will be required: BRCA1,
             BRCA2, ATM, BARD1, BRIP1, CDK12, CHEK1, FANCL, FANCA, PALB2, PPP2R2A, RAD51B, RAD51C,
             RAD51D, and RAD54L. Variants of unknown significance in one of the above genes are not
             eligible.

        Exclusion Criteria

          1. History of myelodysplastic syndrome or acute myeloid leukemia.

          2. During phase 2, patients must not have received previous treatment with a DNA-damaging
             cytotoxic chemotherapy (e.g. prior platinum-based chemotherapy and mitoxantrone are
             not permitted) or PARP inhibitor. Prior treatment with PARP inhibitor is allowed
             during phase I dose escalation.

          3. Untreated leptomeningeal or metastatic CNS disease; patients with treated disease may
             be eligible if clinically stable for 4 weeks after radiation or surgery including
             those with history of spinal cord compression that have received definitive treatment.
             If patients are receiving steroids as adjunct for treatment of leptomeningeal disease
             or metastatic CNS disease, dose should be stable for 4 weeks prior to day 1 of cycle
             1.

          4. Clinically significant, uncontrolled heart disease and/or recent events including any
             of the following:

               -  History of acute coronary syndromes (including myocardial infarction, unstable
                  angina, coronary artery bypass grafting, coronary angioplasty or stenting) or
                  symptomatic pericarditis within 6 months prior to screening

               -  History of documented congestive heart failure (New York Heart Association
                  functional classification III-IV)

               -  History of any cardiac arrhythmias, e.g., ventricular, supraventricular, nodal
                  arrhythmias, or conduction abnormality within 12 months of screening. Patients
                  with rate-controlled atrial fibrillation or flutter are permitted.

               -  QTcF > 470 msec on screening 12-lead ECG

               -  Documented cardiomyopathy

          5. Clinically significant uncontrolled hypertension (systolic blood pressure > 150 mmHg
             or diastolic pressure > 90 mmHg despite optimal medical management). For the purpose
             of this protocol definition of uncontrolled hypertension is based on persistent (≥72
             hours) and symptomatic.

          6. Arterial or venous thrombotic or embolic events such as cerebrovascular accident
             (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism
             within 6 months before the start of study medication. However, patients with a venous
             thrombosis, including a pulmonary embolus, who have been on stable anticoagulation
             (more than 1 month without bleeding on a stable dose) is permitted. Patients with
             evidence or history of uncontrolled bleeding diathesis. Any hemorrhage or bleeding
             event ≥ CTCAE Grade 3 within 4 weeks prior to the start of study medication

          7. History or concurrent condition of clinically significant interstitial lung disease
             and/or severely impaired lung function. History of renal failure requiring peritoneal
             dialysis or hemodialysis. History of cirrhosis Child-Pugh B or C. Intestinal
             malabsorption.

          8. Active, clinically serious infections of CTCAE (v 5.0) Grade ≥ 2 or per investigator
             discretion.

          9. History of uncontrolled human immunodeficiency virus (HIV) infection defined as CD4 <
             200 cells/mm3 or detectable viral load is not allowed.

         10. Hepatitis B (HBV) or hepatitis C (HCV). All patients must be screened for HBV and HCV
             up to 28 days prior to study drug start using the routine hepatitis virus laboratorial
             panel. Patients positive for HBsAg or HBcAb will be eligible if they are negative for
             HBV-DNA. These patients should receive prophylactic antiviral therapy. Patients
             positive for anti-HCV antibody will be eligible if they are negative for HCV-RNA.

         11. Previous or concurrent history of malignancies within 5 years prior to study treatment
             except for curatively treated cervical carcinoma in situ, non-melanoma skin cancer,
             superficial bladder cancer (Ta [non-invasive tumor], Tis [carcinoma in situ] and T1
             [tumor invades lamina propria]) or other T1 tumor that has been surgically removed
             with a low chance of recurrence in the next 3 years.

         12. Known hypersensitivity to any of the test drugs, test drug classes, or excipients in
             the formulation

         13. Ongoing substance abuse, medical, psychological or social conditions that may
             interfere with the patient's participation in the study or evaluation of the study
             results.

         14. Prior radiation within 7 days of start drug. Prior major surgery, open biopsy or
             significant trauma within 28 days of start drug.

         15. Patients with severe psychiatric illness/social situations that would limit compliance
             with study requirements in the judgment of study investigator

         16. Patient has a history of non-compliance to medical regimen or inability to grant
             consent

         17. Ongoing immunosuppressive therapy. Patients may be receiving up to 10mg/day of
             prednisone.

         18. Radiotherapy or immuno-/chemotherapy less than 2 weeks before start of treatment. A
             wash-out period of 2 months from radiopharmaceuticals such as radium-223 and
             177Lu-PSMA among others will be required.

         19. Myeloid growth factors within 14 days prior to treatment.

         20. Blood or platelet transfusion less than 7 days before cycle 1 day 1.

         21. History of having received an allogeneic bone marrow or organ transplant.

         22. Major surgical procedure or significant traumatic injury (as judged by the
             investigator) within 28 days before start of treatment, or have not recovered from
             major side effects; open biopsy within 7 days before start of treatment.

         23. Anti-arrhythmic therapy for ventricular arrhythmias. Use of amiodarone and propafenone
             for atrial fibrillation rate control is allowed.

         24. Use of CYP3A4 inhibitors and inducers. Copanlisib is primarily metabolized by CYP3A4.
             Therefore concomitant use of strong inhibitors of CYP3A4 (e.g., ketoconazole,
             itraconazole, clarithromycin, darunavir, indinavir, lopinavir, mifepristone,
             posaconazole, ombitasvir, idelalisib, cobicistat, atazanavir, ritonavir, indinavir,
             nelfinavir and saquinavir) and inducers (apalutamide, carbamazepine, enzalutamide,
             fosphenytoin, phenobarbital, phenytoin, primidone, rifampin) is not allowed. Rucaparib
             is a moderate inhibitor of CYP1A2 and a weak inhibitor of CYP2C9, CYP2C19 and CYP3A4
             and no specific medications is contra-indicated but dose adjustment may be necessary
             of concurrent medication