Ribociclib in Combination With Everolimus and Dexamethasone in Relapsed ALL

Inclusion Criteria: * Age \> 12 months (365 days) and ≤ 30 years * Histologically confirmed diagnosis of either 1) relapsed or refractory ALL or 2) CML in lymphoid blast crisis (must have failed at least 2 lines of TKI therapy) * Primary refractory disease: Persistent disease after at least two induction attempts * Relapsed disease: Second or subsequent relapse, or any relapse refractory to salvage chemotherapy * Participants must have bone marrow with ≥ 1% lymphoblasts definitively identified either on a bone marrow aspirate or biopsy sample, as assessed by morphology, immunohistochemical studies, flow cytometry, karyotype, cytogenetic testing such as fluorescent in situ hybridization (FISH) or other molecular studies. * Participants with CNS1 or CNS2 disease are eligible. Patients with isolated CNS relapse or CNS 3 disease are not eligible. (Refer to Section 12.4 for definitions of CNS status) * Participants must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study and meet all of the following criteria: * Corticosteroids: 14 days must have elapsed since the completion of systemic corticosteroid administration. The following uses of corticosteroids are permitted: single doses (e.g., during anesthesia), topical applications (e.g., for rash), inhaled sprays (e.g., for obstructive airway diseases, asthma), eye drops or local injections (e.g., intra-articular) * Myelosuppressive chemotherapy: 14 days must have elapsed since the completion of myelosuppressive therapy. Individuals may have received any of the following medications within 14 days without a "wash-out" period: * Standard maintenance therapy, other than corticosteroids (vincristine, 6MP, low dose methotrexate) * Hydroxyurea * Intrathecal chemotherapy with methotrexate, hydrocortisone and/or cytarabine. * Radiation therapy (XRT): * Total Body Irradiation (TBI) or cranial radiation therapy: Must have been completed more than 90 days prior to study entry * XRT for chloroma does not require a washout period. * Palliative XRT does not require a washout * Small molecule inhibitors (BCR-ABL or FLT3 inhibitors, for example): 7 days must have elapsed since the completion of therapy. For agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur. The duration of this interval must be discussed with the Study Chair. * Immunotherapy: At least 6 weeks after the administration of any type of immunotherapy, including, but not limited to, tumor vaccines, chimeric antigen receptor (CAR) therapy, other immune effector cell therapy or checkpoint inhibitors. * Monoclonal antibodies: At least 3 half-lives of the antibody after the last dose of a monoclonal antibody. (See table on DVL homepage listing monoclonal antibody half-lives: https://members.childrensoncologygroup). * Prior hematopoietic stem cell transplant (HSCT): Patients who have received HSCT are eligible, but must meet all of the following conditions: * Autologous HSCT \> 60 days of study entry * Allogeneic HSCT \> 90 days of study entry * No evidence of graft-versus-host-disease (GVHD) * Weaning or stable doses of calcineurin inhibitors are permitted provided there is no evidence of active GVHD. * Participants must have a body surface area (BSA) ≥ 0.4 m2. * Performance status: --Lansky \> 50 for individuals \< 16 years old; Karnofsky \> 50% for individuals ≥ 16 years old (See Appendix A). * Participants must have adequate organ function as defined by the following laboratory values: * Direct bilirubin ≤1.5 X institutional upper limit of normal (ULN). * Alanine aminotransferase (ALT) \< 3 x ULN for age and aspartate aminotransferase (AST) \< 3 x ULN for age. Patients with leukemic infiltration of the liver must have AST and ALT \< 5 x ULN for age. * Creatinine below institutional ULN or creatinine clearance \> 60 mL/min/1.73 m2 for subjects with creatinine levels above institutional normal. * Echocardiogram ejection fraction ≥50%. Echocardiogram must be obtained while patient is not receiving cardiotropic medications (e.g., pressors or afterload reducers). * QTcF \< 450 ms on screening ECG. * Oxygen saturation ≥ 90% by pulse oximetry without administration of supplemental oxygen. * Female patients of childbearing potential must have a negative urine or serum pregnancy test confirmed prior to enrollment. * Female patients with infants must agree not to breastfeed their infants while on this study. * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 21 days after the last dose of the study drug. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * Ability to understand and/or the willingness of the patient (or parent or legally authorized representative, if minor) to provide informed consent, documented using an institutionally approved informed consent procedure. Exclusion Criteria: * Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of ribociclib, everolimus or dexamethasone (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection). * Individuals with CNS 3 leukemia at time of study entry. History of CNS 3 disease is allowable as long as patient meets eligibility criteria (CNS 1 or 2) at time of enrollment. * Individuals with Down syndrome. * Treatment with hematopoietic growth factors (G-CSF): * Long-acting (e.g., Neulasta) within 14 days prior to study entry * Short-acting (e.g., Neupogen) within 7 days prior to study entry * Treatment with an investigational agent within 28 days of study entry, or 3 half-lives, whichever is longer. * Patients will be excluded if there is a plan to administer non-protocol chemotherapy, radiation therapy, or immunotherapy during the study period. * Clinically significant, uncontrolled heart disease and/or cardiac repolarization abnormalities, including any of the following: * History of acute coronary syndromes (including myocardial infarction, unstable angina, coronary artery bypass grafting, coronary angioplasty, or stenting) or symptomatic pericarditis within 6 months prior to screening * History of documented congestive heart failure (New York Heart Association functional classification III-IV) * Cardiomyopathy * Clinically significant cardiac arrhythmias (e.g. ventricular tachycardia), complete left bundle branch block, high-grade AV block (e.g. bifascicular block, Mobitz type II and third-degree AV block) * Long QT syndrome or family history of idiopathic sudden death or congenital long QT syndrome, or any of the following: * Risk factors for Torsades de Pointe (TdP) including uncorrected hypokalemia or hypomagnesemia, history of cardiac failure or history of significant/symptomatic bradycardia. * Concomitant use of medication(s) with a known risk to prolong the QT interval and/or known to cause Torsades de Pointe that cannot be discontinued (within 5 half-lives or 7 days prior to starting study drug) or replaced by safe alternative medication (See Appendix C for list of prohibited medications) * Inability to determine the QTcF interval on screening EKG (using Fridericia's correction) * Prior exposure to a CDK4/6 inhibitor * Patient is currently receiving any of the following medications and cannot be discontinued 7 days prior to starting study drug (see Appendix C for prohibited medications): * Known strong inducers or inhibitors of CYP3A4/5, including grapefruit, grapefruit hybrids, pummelos, star-fruit, and Seville oranges * Medications with a narrow therapeutic window that are predominantly metabolized through CYP3A4/5 * Herbal preparations/medications, dietary supplements. * Patients refractory to red blood cell or platelet transfusions. * Patient is currently receiving warfarin or other coumarin-derived anticoagulant for treatment, prophylaxis or otherwise. Therapy with heparin, low molecular weight heparin (LMWH) or fondaparinux is allowed. * Patients with systemic fungal, bacterial, viral or other infection that is exhibiting ongoing signs/symptoms related to the infection without improvement despite appropriate antibiotics or other treatment. * Patients known to have human immunodeficiency virus (HIV) infection; baseline testing for HIV is not required. * Patients known to have active hepatitis A, B, or C infection; or known to be positive for HCV RNA or HBsAg (HBV surface antigen); baseline testing for viral hepatitis is not required. * Major surgery within 2 weeks of the first dose of study drugs. The following are not considered major surgery for the purposes of eligibility: Tumor biopsy, insertion of a gastric feeding tube, central venous access. * Individuals with significant concurrent disease, illness, psychiatric disorder or social issue that would compromise patient safety or compliance, interfere with consent, study participation, follow up, or interpretation of study results. * Individuals with a history of a different malignancy (other than ALL) are ineligible except for the following circumstances: * Individuals are eligible if they have been disease-free for at least 5 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. * Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: cervical cancer in situ, and basal cell or squamous cell carcinoma of the skin. * Pregnant or nursing women are excluded