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 estimated glomerular filtration rate (eGFR) is \> 60 mL/min
* Hemoglobin \>= 9.0g/dL
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
* Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression
* Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy
* Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
* Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better
* The effects of M1774 on the developing human fetus are unknown. For this reason and because ATR inhibitors may be teratogenic (Musson et al., 2022), women of child-bearing potential who are partners of men enrolled on this protocol must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to the study, for the duration of study participation, and 6 months after completion of M1774 administration. Should a woman become pregnant or suspect she is pregnant while her partner is participating in this study, she should inform her treating physician immediately. Men enrolled on this study must agree to use adequate contraception prior to study entry, for the duration of study participation, and 3 months after completion of M1774 administration
* Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants

Exclusion Criteria:

* Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia
* Patients who are receiving any other investigational agents
* Patients with uncontrolled intercurrent illness
* Patients who cannot discontinue proton pump inhibitors (PPIs). H2 receptor antagonists will not be permitted within 12 hours before dosing of M1774 and until 2 hours after dosing of M1774. Antacids will not be permitted within 2 hours before and 2 hours after administration of M1774
* Patients who cannot discontinue drugs that are strong inhibitors of CYP3A4 or CYP1A2
* Patients who cannot discontinue drugs that are hMATE1 or hMATE2-Ksubstrates
* Patients with a baseline QC interval \> 470 msec