PALBOCICLIB + PD-0325901 for NSCLC & Solid Tumors

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.