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

* INCLUSION CRITERIA: * Participants must have documented 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, defined as at least one lesion on TC99 bone scan or at least one lesion that is measurable per, per RECIST 1.1. * mCSPC participants: * Participants must be within 134 days of starting ADT. * If participants are on ADT and responding, this may impact the findings on scans. Pre- treatment scans could be used to confirm that participants have metastatic high-volume disease in such cases. * For Cohorts 1 and 2, Dose escalation and Safety Run-in, only: mCSPC may have high or low volume disease. * For Cohort 3, Dose Expansion: mCSPC participants must have high volume disease (as defined by visceral lesion or 4 or greater bone lesions, at least one of which is beyond the spine and pelvis). * mCRPC participants: * Must need ADT as part of their cancer therapy (unless previous orchiectomy) * Must have been previously treated with modern anti-androgens such as abiraterone, enzalutamide, apalutamide, or darolutamide. * Must have not had progression while on docetaxel if given for mCSPC or within 3 months of completing docetaxel for mCSPC. * Progression defined as either rising PSA greater than 2.0 ng/ml or radiographic evidence of progression seen on CT scan or TC-99 bone scan. * Toxicities related to prior therapy, including surgery and/ or radiation, must have resolved to \<= grade 1. * Men age \>=18 years. Because no dosing or adverse event data are currently available on the use ofINCLUSION CRITERIA: * Participants must have documented 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, defined as at least one lesion on TC99 bone scan or at least one lesion that is measurable per, per RECIST 1.1. * mCSPC participants: * Participants must be within 134 days of starting ADT. * If participants are on ADT and responding, this may impact the findings on scans. Pre- treatment scans could be used to confirm that participants have metastatic high-volume disease in such cases. * For Cohorts 1 and 2, Dose escalation and Safety Run-in, only: mCSPC may have high or low volume disease. * For Cohort 3, Dose Expansion: mCSPC participants must have high volume disease (as defined by visceral lesion or 4 or greater bone lesions, at least one of which is beyond the spine and pelvis). * mCRPC participants: * Must need ADT as part of their cancer therapy (unless previous orchiectomy) * Must have been previously treated with modern anti-androgens such as abiraterone, enzalutamide, apalutamide, or darolutamide. * Must have not had progression while on docetaxel if given for mCSPC or within 3 months of completing docetaxel for mCSPC. * Progression defined as either rising PSA greater than 2.0 ng/ml or radiographic evidence of progression seen on CT scan or TC-99 bone scan. * Toxicities related to prior therapy, including surgery and/ or radiation, must have resolved to \<= grade 1. * Men age \>=18 years. Because no dosing or adverse event data are currently available on the use of PDS01ADC in combination with docetaxel in participants \<18 years of age, children are excluded from this study. * ECOG performance status 0-2. * Participants must have adequate organ and marrow function as defined below: * Absolute neutrophil count \>=1,500/mcL, without CSF support * Platelets \>=100,000/mcL * Hemoglobin \>9 g/dL * PT \<= 1.5 x ULN * aPTT \<= 1.5 x ULN * Total bilirubin \<= upper limit of normal (ULN), OR in participants with Gilbert's syndrome, a total bilirubin \<= 3.0 * Serum albumin \>=2.8 g/dL * AST(SGOT)/ALT(SGPT) \<=1.5 X institutional upper limit of normal \-- Hepatic function based on Child-Pugh Class: Participants with hepatic impairment must have Child-Pugh Class A or better * Serum Creatinine OR Creatinine Clearance \<= 1.5 X institutional upper limits of normal OR \>=50 mL/min/1.73 m\^2 calculated by eGFR in the clinical lab for participants with serum creatinine levels \> 1.5 ULN * The effects of PDS01ADC in combination with docetaxel and abiraterone on the developing human fetus are unknown. For this reason and because docetaxel agents as well as other immuno-therapeutic agents used in this trial are known to be teratogenic, sexually active subjects and their female partners must agree to use medically accepted barrier methods of contraception (e.g., male or female condom)after enrollment on study , during the study treatment and for 4 months after the last dose of abiraterone, docetaxel or PDS01ADC, even if oral contraceptives are also used. Should a woman become pregnant or suspect she is pregnant while her partner is participating in this study, she should inform her treating physician immediately and her partner should inform the study doctor immediately. * Ability of subject to understand and the willingness to sign a written informed consent document. Subject should be willing to travel to the NIH for follow-up visits. * Participants with prior immune checkpoint therapy are eligible to enroll upon PI discretion. EXCLUSION CRITERIA: * Immunocompromised status due to: * Human immunodeficiency virus (HIV) positivity * Active autoimmune diseases such as Addison's disease, Hashimoto's thyroiditis, systemic lupus erythematosus, Sjogren syndrome, scleroderma, myasthenia gravis, Goodpasture syndrome or active Grave's disease. Participants with a history of autoimmunity that has not required systemic immunosuppressive therapy or does not threaten vital organ function including CNS, heart, lungs, kidneys, skin, and GI