Study of Apalutamide With Carotuximab in Metastatic, Castration-Resistant Prostate Cancer

Inclusion Criteria: * History of castration-resistant prostate cancer with rising PSA (prostate-specific antigen) on a contemporary ARSI (Androgen receptor (AR) signaling inhibitor: abiraterone, enzalutamide, darolutamide). Bicalutamide, nilutamide, and flutamide will not be considered as contemporary ARSIs * Patient must have had 1 and can have up to 2 prior AR targeted therapy with the exception of apalutamide. * Patients must decline or be ineligible for taxane therapy in the opinion of the treating physician. * 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 and/or carotuximab) Exclusion Criteria: * Non-PSA producing prostate cancers such as small cell prostate cancers or those prostate cancers which exhibit radiographic progression without PSA rise * Prior use of apalutamide * Other prior malignancy requiring active anticancer therapy * Prior exposure to carotuximab or any CD105 targeted antibody * Active bleeding or pathologic medical conditions that carries a high bleeding risk * A known diagnosis of Osler-Weber-Rendu syndrome