This is a clinical trial for adult men diagnosed with progressive metastatic castration-resistant prostate cancer. 
   
The main purpose of this study is to evaluate the maximum tolerated and recommended dose of pembrolizumab and an androgen-receptor pathway inhibitor with or without the investigational drug 225Ac-J591 to see what its side effects are and if it works for this type of cancer.

Investigational means that 225Ac-J591 is not yet approved by the United States Food and Drug Administration (FDA).
   
The study has two phases. In the first phase, small groups of participants will receive combined therapy with pembrolizumab and an oral hormonal agent with one of two different dose levels of 225Ac−J591, one low dose and one moderate dose.
   
In the second phase of the study, participants will receive pembrolizumab 400 mg every 6 weeks plus a standard oral hormonal drug. Pembrolizumab will be administered by infusion into a vein.
   
Participants will be randomized to also either receive a dose of 225Ac-J591 or not. Randomization is like flipping a coin and there is a 50/50 chance of being assigned the infusion or not. If assigned to receive it, 225Ac-J591 will be given as a single intravenous dose plus IV fluids. 
   
Participants may receive up to one treatment of 225Ac-J591 and up to approximately 2 years of pembrolizumab in this study. Participants will be on the oral hormonal drug indefinitely as long as the study team thinks that they are benefiting without significant side effects.