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: Metastatic castration sensitive and castration resistant prostate cancer (mCSPC and mCRPC) are prostate cancers that have spread to other parts of the body. Use of the drug docetaxel with androgen deprivation therapy can improve survival for men with mCSPC. Researchers want to see if combining this treatment with other drugs can help delay the time it takes for mCSPC and mCRPC to get worse. Objective: To learn if giving docetaxel with PDS01ADC is safe and effective for men with prostate cancer. Eligibility: Men age 18 and older with mCSPC or mCRPC. Design: Participants will be screened with a medical history and physical exam. Their diagnosis will be confirmed. Their symptoms and how well they do their normal activities will be reviewed. They will have blood and urine tests. Their heart will be evaluated. They will have imaging scans of the chest, abdomen, and pelvis. They will have bone scans with intravenous (IV) injections of Tc99 to check for tumor spread in the bones. Some screening tests will be repeated during the study. Participants may have tumor biopsies. Participants will get treatment in cycles. Each cycle will last 21 days. They will get docetaxel through IV infusion. They will get PDS01ADC as an injection under the skin. Participants with mCSPC will have up to 6 cycles. Those with mCRPC will be treated until they cannot tolerate the side effects or their disease gets worse. Participants will have a follow-up visit 30 days after treatment ends. Those with mCSPC will then have follow-up visits at the clinic every 3 months....

* 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 \=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 \=18 years. Because no dosing or adverse event data are currently available on the use of PDS01ADC in combination with docetaxel in participants \=1,500/mcL, without CSF support * Platelets \>=100,000/mcL * Hemoglobin \>9 g/dL * PT \170/ DBP\>105) * Has received or will receive a live vaccine within 30 days prior to the first administration of study intervention. Seasonal flu vaccines that do not contain a live virus are permitted. Locally approved COVID vaccines are permitted. * Participants who have had prior docetaxel for mCRPC * mCSPC participants will be excluded if they did not start abiraterone within 6 weeks of ADT and/or had any docetaxel * Participants who have had progression within 3 months of completing docetaxel for mCSPC * History of allergic reactions attributed to compounds of similar chemical or biologic composition to PDS01ADC investigational agents used in the study * The subject has had evidence within 3 years of the start of study treatment of another active malignancy which required systemic treatment (except for nonmelanoma skin cancers or carcinoma in situ of the bladder). * The subject has active brain metastases or epidural disease. * Participants with greater than or equal to grade 2 peripheral neuropathy (defined by CTCAE 5.0) at baseline.