Study of JAK Inhibition in Stem-Like Prostate Cancer (JASPER): A Phase 1b/2a Multicenter Study of Ruxolitinib and Enzalutamide in Castration Resistant Prostate Cancer

Inclusion Criteria: * Written informed consent and Health Insurance Portability and Accountability Act (HIPAA) authorization for release of personal health information prior to registration * Males age ≥ 18 years with progressive metastatic, castration-resistant prostate cancer, previous adenocarcinoma histology confirmation required * Ability to understand a written informed consent document, as determined by the study physician or designee * Surgical castration or continuous medical castration ≥ 8 weeks prior to screening; serum testosterone \< 50 ng/dL * Have progressed on prior abiraterone treatment by Prostate Cancer Working Group 3 prostate specific antigen (PSA) criteria * PSA must rise on two measurements at least 1 week apart in order to be eligible. Refer to PCWG3 for clarification. * Most Recent absolute PSA must be \> 2.0 ng/mL * Patient meets definition of poor responder to abiraterone by one of the following: * Abiraterone started in hormone-sensitive prostate cancer (HSPC) disease setting (abiraterone started within 4 months of starting continuous androgen deprivation therapy \[ADT\]): \< 12 months duration on abiraterone * Abiraterone started in castration-resistant prostate cancer (CRPC) disease setting: \< 6 months duration on abiraterone due to progression or failure to achieve PSA50 response while on therapy * The patient's current or most recent treatment is ADT and abiraterone. Participants must sign consent within 30 days of discontinuing abiraterone or prior to stopping abiraterone * Patients must be willing to undergo metastatic tumor biopsy during screening. If no metastatic lesion is safely accessible to tumor biopsy, this requirement will not be required * 50% of patients must have measurable disease by RECIST 1.1 criteria * Once 50% of total expected cohort has non-measurable disease, only patients with measurable disease by RECIST 1.1 criteria will be eligible. (Percentages with measurable disease are not relevant within dose escalation. Once dose expansion is started, those at expansion dose would be included in percentage evaluation.) * Eastern Cooperative Oncology Group (ECOG) performance status of 0 - 2 (grade 2 ECOGs should be related to disease and thus potentially reversible) * A male participant must agree to use of contraception during the treatment period and for at least 90 days after the last dose of study drug. Female partners of male patients should also use contraception for 90 days after the last dose of study drug if they are of childbearing potential * Platelets ≥ 125,000/mm\^3 (obtained within 28 days prior to starting study therapy) (if creatinine clearance \[CrCl\] is between 30-59, the platelet entry criteria is \> 150,000/mm\^3) * Absolute neutrophil count (ANC) ≥ 1500/mm\^3 (obtained within 28 days prior to starting study therapy) * Hemoglobin ≥ 11 g/dL (obtained within 28 days prior to starting study therapy) No transfusions within 90 days prior to screening unless performed for acute bleeding * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) ≤ 3 x upper limit of normal (ULN) (obtained within 28 days prior to starting study therapy) For patients with known liver metastasis: (ALT) and aspartate aminotransferase (AST) ≤ 5 x ULN * Bilirubin ≤ 1.5 the upper limit of normal (ULN) OR direct bilirubin ≤ ULN for participants with total bilirubin levels \> 1.5 x ULN. For subjects with known Gilbert's disease, bilirubin ≤ 3.0 mg/dL (obtained within 28 days prior to starting study therapy) * Creatinine clearance (CrCl) ≥ 30 mL/min (obtained within 28 days prior to starting study therapy) For creatinine clearance estimation, the Cockcroft and Gault equation should be used Exclusion Criteria: * History of untreated (with radiotherapy and/or surgery) brain metastasis is not allowed (stable and treated metastases are allowed) * History of seizures or known hypersensitivity to enzalutamide, ruxolotinib or any of the excipients in the product * Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with the absorption of the study medications * Uncontrolled hypertension as indicated by systolic blood pressure (SBP) \> 170 mmHg or diastolic blood pressure (DBP) \> 105 mmHg on 2 consecutive measurements at screening visit unless known to have white coat hypertension syndrome * Have received chemotherapy in the metastatic castration-resistant setting (docetaxel within the hormone sensitive setting is allowed) * Failure to recover to grade 1 or lower toxicity related to prior systemic therapy (excluding alopecia and neuropathy) prior to study consent * Current active infection with any of the following: hepatitis B, hepatitis C, active tuberculosis, latent tuberculosis. Patients with well controlled HIV are eligible however all drug interactions with HIV drug and study therapies have to be reviewed * History of myocardial infarction, stroke, pulmonary embolism or deep vein thrombosis within 6 months of study enrollment * Study physician estimates life expectancy less than 6 months or patient is unable to swallow medications * Patients currently taking fluconazole * Currently receiving supplements containing androgens or medications known to be strong inhibitors of CYP2C8, strong inducers (except enzalutamide) or strong inhibitors of CYP3A4 and substrates of CYP3A4, CYP2C9 and CYP2C19 with a narrow therapeutic window. If substitution is possible, strong inducers, inhibitors and substrates must be discontinued at least 7 days or 5 half-lives (which ever longer) prior to the first administration of enzalutamide * Due to risk of tuberculosis (TB) reactivation, patients deemed at high risk by treating provider (e.g., close contact with someone with active TB, history of active/latent TB) should be excluded * Those with underlying hepatic disease with a CHILD-PUGH class A, B or C impairment are excluded