A Phase I/II Study of PDS01ADC With Docetaxel and Abiraterone in Adults With Metastatic Castration Sensitive and PDS01ADC With Docetaxel in Castration Resistant Prostate Cancer

Background: * A phase III trial demonstrated that combining docetaxel and androgen deprivation therapy (ADT) significantly improved survival (57.6 vs 44.0 months (hazard ratio HR=0.56, (0.44- 0.70), p \<0.0001) for men with metastatic castration sensitive prostate cancer (mCSPC). The greatest benefit was seen in men with high volume disease (visceral disease or 4+ bone lesions with at least one beyond the pelvis and spine.) * Docetaxel has limited efficacy in metastatic castration resistant prostate cancer (mCRPC) patients who have already progressed on anti-androgen therapy (abiraterone or enzalutamide). * Intensification of treatment in de novo mCSPC patients by adding abiraterone to docetaxel and ADT has been shown in a phase III trial to significantly improve OS (0.82, (0.69 - 0.98) p=0 (Summation)030) and rPFS (HR=0.54,(0.41-0.71) p \<0.0001) * Clinical data have indicated that PSA \<=0.20 ng/ml eight months after starting androgen deprivation therapy (ADT) is prognostic for overall survival based on data from the phase III trial. * Preclinical data demonstrates that docetaxel increases uptake of PDS01ADC, an IL-12 immunocytokine that targets necrosis. * Additional preclinical data demonstrates the potential anti-tumor synergy of PDS01ADC when combined with docetaxel. Objectives: Phase I: To evaluate safety and tolerability of docetaxel in combination with PDS01ADC in participants who have metastatic prostate cancer. Phase II: -Determine clinical efficacy in adults with prostate cancer treated when standard of care is combined with PDS01ADC. For mCSPC the standard of care is docetaxel + abiraterone. For mCRPC the standard of care is docetaxel. * For mCSPC participants: Clinical efficacy will be measured by prostate specific antigen (PSA \<0.2 ng/ml) eight months after start of androgen deprivation therapy (ADT). * For mCRPC participants: Clinical efficacy will be measured by an increase in their median progression free survival (PFS). Eligibility: * Men age \>=18 years * Histopathological confirmation of prostate cancer. If no pathologic specimen is available, participants may enroll with a pathologist s report showing a histologic diagnosis of prostate cancer and a clinical course consistent with the disease. * Participants must have metastatic disease * mCSPC participants must be within 134 days of starting ADT. * mCRPC participants must have been previously treated with ADT. Design: * Open-label, single-center, non-randomized Phase I/II study * To ensure safety of the combination before using in larger numbers of mCSPC and mCRPC participants, PDS01ADC will be escalated from a starting dose of 12 mcg/kg and a second dose level of 16.8 mcg/kg along with docetaxel. mCSPC participants will receive a maximum of 6 cycles. mCRPC participants will continue until progression or unacceptable toxicity. * The remaining participants will be enrolled onto the trial in the following expansion cohorts, each of which will receive the determined safe dose of PDS01ADC. ADT will be maintained/given per standard of care throughout the study. * mCSPC participants: Once ADT established, simultaneous docetaxel 75 mg/m\^2 (given every 3 weeks x 6 cycles starting at Cycle 1), with PDS01ADC at the RP2D, given every 3 weeks from cycle 2 through cycle 6). Abiraterone will be given in addition to docetaxel from the start of cycle 1 at a dose of 1000mg by mouth once daily. Prednisone will be given orally at 5 mg twice a day and will not be optional. * The first 6 participants in the mCSPC arm including abiraterone will be evaluated as a safety lead-in of PDS01ADC at 12 mcg/kg. If there are 2 or more DLTs within these initial 6, then the doses will be de-escalated and 6 additional participants will be evaluated at this lower dose of PDS01ADC at 8 mcg/kg. * mCRPC participants: docetaxel 75 mg/m\^2 (given every 3 weeks starting at Cycle 1) with PDS01ADC at the RP2D, given every 3 weeks from cycle 2 onwards until disease progression or unacceptable toxicity. Prednisone will be given 5 mg twice a day for each dose or 10 mg once a day. * It is anticipated that approximately 4 years may be required for accrual of up to 80 participants.