We are doing this study to find out if the study drug, pembrolizumab, is a safe and effective treatment for metastatic castrate-resistant prostate cancer when it is given in different combinations with other drugs. Pembrolizumab may work by increasing your immune system's response against a tumor.

Metastatic Castrate-Resistant Prostate Cancer

Adults ages 18+ who:

• Are diagnosed with a type of metastatic castrate-resistant prostate cancer called "neuroendocrine carcinoma"
• Have previously been treated with a drug called docetaxel

For more information about who can join this study, please contact the study team at julia.hurrelbrink@duke.edu.

If you choose to join this study, you will:

• Be assigned to take the study drug, pembrolizumab, in combination with lenvatinib, or MK-7684, or carboplatin + etoposide
• Have blood draws
• Give urine samples
• Have imaging scans (CT and/or MRI)

Pembrolizumab, MK-7684, etoposide, and carboplatin are all drugs taken intravenously (through a needle in a vein in your arm). Lenvatinib is a pill that you take by mouth.