Ruxolitinib Phosphate or Dasatinib With Chemotherapy in Treating Patients With Relapsed or Refractory Philadelphia Chromosome-Like Acute Lymphoblastic Leukemia

Inclusion Criteria: * Patients with previously treated B-cell ALL (relapsed and/or refractory after prior therapy) * Bone marrow involvement with \>= 5% lymphoblasts * Documented genetic lesion(s) known to confer susceptibility to inhibition by either ruxolitinib or dasatinib or cytokine receptor-like factor 2 (CRLF2) positivity by flow cytometry (for the ruxolitinib cohort) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Total bilirubin \< 2.0 mg/dL * Serum glutamate pyruvate transaminase (SGPT) or serum glutamic oxaloacetic transaminase (SGOT) \< 3 x upper limit of normal (ULN) * Creatinine \< 2 mg/dL * Females of childbearing potential must have a negative serum or urine beta human chorionic gonadotropin (beta-hCG) pregnancy test result within 14 days prior to the first dose of study drugs and must agree to use an effective contraception method during the study and for 30 days following the last dose of study drug; females of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy; appropriate methods of birth control include the following: any 2 of the following methods used together: birth control implants, injections, or pills (except for progesterone only pills), intrauterine device (IUD), vasectomy, tubal ligation, barrier method (female or male condom with spermicide, cervical cap with spermicide, diaphragm with spermicide); male condom with spermicide and diaph…