This research study is evaluating the experimental drug palbociclib in combination with another experimental drug PD-0325901 as a possible treatment for cancers with KRAS mutations, particularly for those which started in the lung.

This will be an open label Phase I dose escalation study evaluating the combination of the CDK4/6 inhibitor palbociclib (PD-0332991) and the MEK inhibitor PD-0325901. To determine the maximally tolerated dose (MTD) and recommended phase 2 dose (RP2D), a 3+3 dose escalation protocol will be undertaken. Once the RP2D has been determined, the study will then evaluate, in a randomized phase II study design, the combination of palbociclib and PD-0325901 compared to PD-0325901 alone and palbociclib alone in KRAS mutant NSCLC.

• Phase 1: The investigators are looking for the highest dose of the study drug that can be administered safely without severe or unmanageable side effects in participants that have cancer, not everyone who participates in this research study will receive the same dose of the study drug. The dose the participant receives will depend on the number of participants who have been enrolled in the study before and how well the dose has been tolerated.
• Study Drug(s): The participant will be given a study drug-dosing calendar for each treatment cycle. Each treatment cycle lasts 4 weeks during which time you will be taking the study drug for 3 weeks at a time. The participant will take Palbociclib by mouth once a day, every day for 3 weeks. The participant will take PD-0325901 by mouth twice a day, every day for 3 weeks.
• Clinical Exams: During all cycles the participant will have a physical exam and will be asked questions about general health and specific questions about any problems that they might be having and any medications they may be taking.
• Scans (or Imaging tests): The investigators will assess the participant's tumor by either a CT scan or MRI
• Blood Tests: These are special tests to check the amount of drug and the amount of tumor DNA in the participant's blood at specific points in time.

Secondary Outcomes:

• Evaluate PK parameters for the combination of palbociclib and PD-0325901
• Confirm target engagement of palbociclib and PD-0325901 in patients undergoing pre- and on-treatment biopsies in an expansion cohort at the MTD
• Evaluate preliminary clinical efficacy of the combination of palbociclib and PD-0325901 in patients with tumors harboring KRAS mutations.

Inclusion Criteria:

• Dose-escalation/MTD cohorts, participants must have histologically confirmed malignancy with a RAS mutation that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective. For the randomized phase 2 component of the study, participants must have histologically confirmed NSCLC with a confirmed KRAS mutation (via any CLIA-certified method)
• For the dose-escalation component, participants are required to have only evaluable disease. For the MTD cohort and phase 2 component of the study, participants must have measurable disease.
• Participants enrolled to the MTD cohort must agree to pre and on-treatment tumor biopsies if assessable disease is identified.
• Age ≥18 years.
• ECOG performance status ≤ 2 (see Appendix A).

Participants must have normal organ and marrow function as defined below:

• Absolute neutrophils count ≥ 1,500/mcL
• Platelets ≥100,000/mcL
• total bilirubin within normal institutional limits
• AST (SGOT)/ALT (SGPT) ≤ 2.5 X institutional upper limit of normal (≤ 5.0 X institutional upper limit of normal permitted if hepatic metastases present)
• Creatinine within 1.5x the ULN institutional limits.
• Women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation. Ability to understand and the willingness to sign a written informed consent document.
• QTc ≤480 msec.
• The availability of archival tissue to evaluate retrospectively the participant's Rb status
• Patients must have recovered to ≤ Grade 1 in terms of toxicity from prior treatments (excluding neuropathy which can be ≤ Grade 2).

Exclusion Criteria:

• Participants who have had chemotherapy or radiotherapy within 3 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier.
• Participants may not be receiving any other study agents concurrently with the study drugs.
• Participants with symptomatic brain metastases that require chronic steroids are excluded. Patients with a history of brain metastases are permitted to enroll as long as they have been treated, off of steroids and have been stable for one month on imaging.
• Concurrent use with strong CYP3A4 inhibitors/inducers is prohibited due to drug-drug interactions with palbociclib.
• Due to potential drug interactions between warfarin and PD-0325901, warfarin use is excluded. Other anticoagulants are permitted.
• Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
• Pregnant women are excluded from this study because the study agents have the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk of adverse events in nursing infants secondary to treatment of the mother with the study agents, breastfeeding should be discontinued.
• For Part II only: Individuals with a history of a different malignancy are ineligible except if they have been disease-free for at least 2 years and are deemed by the investigator to be at low risk for recurrence. 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.
• HIV-positive individuals on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions.
• Evidence of visible retinal pathology on screening ophthalmologic examination that places the participant at an unacceptable risk for ocular toxicity, such as risk factors for retinal vein occlusion, related to PF-0325901.