Testing the Effect of M1774 on Hard-to-Treat Refractory SPOP-mutant Prostate Cancer

Inclusion Criteria: * Presence of SPOP mutations in prostate cancer cells, as indicated by Next Generation Sequencing (NGS) * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) by chest x-ray or as \>= 10 mm (\>= 1 cm) with CT scan, MRI, or calipers by clinical exam * Castrate-range testosterone (=\< 50 ng/dL) after androgen deprivation therapy (ADT) or orchiectomy * Prior treatment with second generation anti-androgen (2GAA) and taxane- or lutetium-based therapy. More than one kind of prior treatment with 2GAA and taxane - or lutetium-based therapies is also acceptable * Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of M1774 in patients \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase \[SGOT\]) or alanine aminotransferase (ALT)(serum glutamic-pyruvic transaminase \[SGPT\]) =\< 3 x institutional upper limit of normal (ULN) * Creatinine =\< 1.5 × ULN * Creatinine clearance \>= 60 mL/min * Creatinine clearance should be measured if es…