PALBOCICLIB + PD-0325901 for NSCLC & Solid Tumors

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.