Study of AR Suppression With Carotuximab in Metastatic, Castration-Resistant Prostate Canc

Inclusion Criteria: * History of castration-resistant prostate cancer with rising PSA on a contemporary ARSI (e.g. abiraterone or, enzalutamide, darolutamide). Bicalutamide, nilutamide, and flutamide will not be considered as contemporary ARSIs. * PSA rise will be defined as an increase in PSA of 0.2 ng/mL or higher on at least 2 separate occasions greater than 1 week apart while on an ARSI * Patient must be surgically castrated or have serum testosterone concentrations much be consistent with castrate levels of testosterone (under 50 ng/dL) while on LHRH analog therapy * Patient must have had 1 and can have up to 2 prior AR targeted agents (if patients have had previous enzalutamide, they will be considered only for arm C). therapy with the exception of apalutamide. * Patients may not have had previous chemotherapy with the exception of docetaxel administered for castration-sensitive disease. * Patients must decline or be ineligible for taxane therapy in the opinion of the treating physician. * Have Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0-1 * Resolution of adverse events results as described below: * If the subject's patient's most recent line of therapy is treatment with abiraterone or enzalutamide, then all adverse events must be resolved to Grade 2 or less * If the subject's patient's most recent line of therapy is any other treatment for mCRPC then all Adverse events must be resolved to grade 1 or less, with the exception of fatigue, alopecia and neuropathy (which must resolve to CTCAE grade 2) * Adequate organ function * All patients must agree to use an adequate method of contraception, in the opinion of the treating investigator, while on protocol treatment and for 3 months after the last dose of protocol treatment (apalutamide/enzalutamide and/or carotuximab) * Written informed consent obtained from subject and ability for subject to comply with the requirements of the study Exclusion Criteria: * Non-PSA producing prostate cancers such as small cell prostate cancers or those prostate cancers which exhibit radiographic progression without PSA rise * Other prior malignancy requiring active anticancer therapy * Prior exposure to carotuximab or any CD105 targeted antibody * Any major surgical procedure, in the opinion of the treating physician, within 2 weeks of starting therapy * Uncontrolled chronic hypertension defined as sustained systolic pressure (SBP) \>150 mmHg or diastolic pressure (DBP) \>90 despite optimal therapy * Active bleeding or pathologic medical conditions, including but not limited to factor deficiencies, hemophilia, etc., that carries a high bleeding risk * Use of thrombolytics within 10 days prior to the first day of carotuximab * Known hypersensitivity to Chinese hamster ovary products or other recombinant human, chimeric, or humanized antibodies * A known diagnosis of Osler-Weber-Rendu syndrome * Ascites or pericardial or pleural effusion requiring external drainage procedures * History of untreated brain involvement with cancer, spinal cord compression, or carcinomatous meningitis, or new evidence of brain or leptomeningeal disease. Patients with radiated or resected lesions are permitted, provided the lesions are fully treated and inactive, patients are asymptomatic, and no steroids have been administered for at least 28 days. Imaging for CNS disease will not be required for screening unless there is a history of a neurological finding such as new onset of weakness or numbness that cannot be explained by other medical history. * Acute cardiovascular event within the past 6 months. An acute cardiovascular event will be defined as a myocardial infarction, NYHA Class II or worse congestive heart failure, cerebrovascular accident, transient ischemic attack, arterial embolism, pulmonary embolism, percutaneous transluminal coronary angioplasty (PTCA), or CABG. * Deep venous thrombosis within the past 6 months, unless the patient is anti-coagulated without the use of warfarin for at least 2 weeks. In this situation, low molecular weight heparin is preferred but clearance should be given by the local PI.