This phase I trial studies the side effects and best dose of palbociclib when given alone and in combination with sorafenib, decitabine, or dexamethasone in treating patients with leukemia that has come back (recurrent) or that does not respond to previous treatment (refractory). Palbociclib, sorafenib, and decitabine may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as dexamethasone, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving palbociclib alone and in combination with sorafenib, decitabine, or dexamethasone may work better in treating patients with recurrent or refractory leukemia.

PRIMARY OBJECTIVES:

I. To determine the maximum tolerated dose (MTD) and dose limiting toxicities (DLT) of various combinations with palbociclib in patients with relapsed and refractory leukemias.

SECONDARY OBJECTIVES:

I. To assess pharmacodynamic effects of palbociclib on the Cyclin-CDK-Rb axis in leukemic blasts of patients with relapsed/refractory (R/R) leukemias.

II. To explore the efficacy (complete response [CR], complete remission without platelet recovery [CRp], complete remission without blood count recovery [CRi], partial response [PR], or clinical benefit [CB]) of palbociclib as a single-agent and in combinations in patients with R/R leukemias.

III. To explore biomarkers of response and resistance in patients with R/R leukemias treated with palbociclib.

IV. To assess the safety and tolerability of one cycle of single-agent palbociclib in patients with R/R leukemias.

OUTLINE: This is a dose-escalation study of sorafenib, decitabine, and dexamethasone. Patients are assigned to 1 of 3 arms.

ARM I: Patients receive palbociclib orally (PO) once daily (QD) on days 1-28. Patients also receive sorafenib PO QD on days 1-28 beginning on cycle 2. Treatment repeats every 28 days for up to 8 cycles in the absence of disease progression or unacceptable toxicity.

ARM II: Patients receive palbociclib as in Arm I. Beginning cycle 2, patients receive palbociclib PO QC on days 1-7 and decitabine intravenously (IV) QD over 1 hour on days 8-17 of cycle 2 and days 8-12 of cycles 3-8. Treatment repeats every 28 days for up to 8 cycles in the absence of disease progression or unacceptable toxicity.

ARM III: Patients receive palbociclib as in Arm I. Patients also receive dexamethasone PO QD or IV over 15-30 minutes on days 1-4 and 15-18 beginning on cycle 2. Treatment repeats every 28 days for up to 8 cycles in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up periodically.

Inclusion Criteria:

1. Participants with a diagnosis of histologically confirmed relapsed or refractory (R/R) acute myeloid leukemia or R/R acute lymphoblastic leukemia for which no available standard therapies are indicated or anticipated to result in a durable response.

2. Only participants with R/R ALL will be eligible for cohort C

3. Age >/= 15 years.

4. Participants must not have had leukemia therapy for 14 days prior to starting palbociclib. However, participants with rapidly proliferative disease may receive hydroxyurea as needed until 24 hours prior to starting therapy on this protocol and starting the first cycle of study.

5. Adequate organ function as defined below:

   • liver function (bilirubin < 2mg/dL, AST and/or ALT <3 x ULN - or <5 x ULN if related to leukemic involvement)
   • kidney function (creatinine < 1.5 x ULN ).
   • known cardiac ejection fraction of > or = 45% within the past 3 months

6. ECOG performance status of ≤ 2.

7. A negative urine pregnancy test is required within 1 week for all women of childbearing potential prior to enrolling on this trial.

8. Participants must have the ability to understand the requirements of the study and signed informed consent. A signed informed consent by the participants or his legally authorized representative is required prior to their enrollment on the protocol.

Exclusion Criteria:

1. Participants women are excluded from this study because the agent used in this study has the potential for teratogenic or abortifacient effects. Because there is a potential risk for adverse events in nursing infants secondary to treatment of the mother with the chemotherapy agents, breastfeeding should also be avoided.
2. Uncontrolled intercurrent illness including, but not limited to active uncontrolled infection, symptomatic congestive heart failure (NYHA Class III or IV), unstable angina pectoris, clinically significant cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
3. Participant with documented hypersensitivity to any of the components of the therapy program.
4. Participants with active, uncontrolled CNS leukemia will not be eligible.
5. Men and women of childbearing potential who do not practice contraception. Women of childbearing potential and men must agree to use contraception prior to study entry and for the duration of study participation.
6. Participants with known history of serous retinopathy will not be eligible.
7. Prior treatment with palbociclib,