Study For Patients With NSCLC EGFR Mutations (Del 19 or L858R +/- T790M)

Partial Inclusion criteria: Evidence of histologically or cytologically confirmed diagnosis of locally advanced or metastatic EGFRm (del 19 or L858R) NSCLC: 1. As detected by local EGFR mutation test that includes QIAGEN therascreen EGFR RGQ PCR kit, Roche cobas® EGFR Mutation Test or a sponsor-approved laboratory developed test that is validated in a CLIA laboratory (with tissue submitted for central laboratory confirmation via FDA approved QIAGEN therascreen RCQ PCR kit). 2. T790M disease as follows: Phase 1 If a repeat biopsy was performed on the tumor following prior EGFR TKI therapy, then T790M positive disease must be present. Patients of unknown T790M status following EGFR TKI progression (ie, no post EGFR TKI progression biopsy was performed) are eligible. In the PK sub-studies involving food/antacid and CYP3A4 effects, patients with EGFRm (del 19 or L858R) with any T790M status are eligible to enroll. Studies at RP2D Cohort 1: Patients may have de novo T790M mutation, but it is not required. Cohort 2 and Cohort 3: Patients must have EGRFm (del 19 AND T790M or L858R AND T790M) NSCLC tumors as detected by local EGFR mutation test that includes QIAGEN Therascreen EGFR RGQ PCR kit, Roche cobas® EGFR Mutation Test or a sponsor-approved laboratory developed test that is validated in a CLIA laboratory, which will then be retrospectively confirmed by the central validated Thermo Fisher Scientific Oncomine Next Generation Sequencing (NGS) cancer panel test. Patients will also be enrolled if they solely test positive for EGFR (del 19 AND T790M or L858R AND T790M) NSCLC in plasma detected by local EGFR mutation test that includes QIAGEN Therascreen EGFR Plasma RGQ kit, Roche cobas® EGFR mutation test v2 (US-IVD) or Sysmex Inostic's OncoBEAMTM EGFR test or a sponsor-approved laboratory developed test that is validated in a CLIA laboratory, which will then be retrospectively confirmed by a validated cfDNA test as determined by the Sponsor. 3. Prior treatment for EGFRm NSCLC as follows: Phase 1 Has progressed after at least 1 prior line of therapy including and EGFR TKI. Patients may have also received other lines of therapy before or after the EGFR TKI. Studies at RP2D Cohort 1: no prior treatment for locally advanced or metastatic EGFRm NSCLC. Cohorts 2 and 3: must have had disease progression on treatment with an approved 1st or 2nd generation EGFR TKI. Patients who have been treated with a 3rd generation EGFR TKI are ineligible for this study. Patients may have had multiple lines of therapy; however, the last therapy prior to study treatment must have been an approved EGFR TKI and received within 6 weeks prior to study registration. Patients must have at least one measurable lesion as defined by RECIST version 1.1 that has not been previously irradiated. Tumor tissue available. Requesting formalin fixed paraffin embedded (FFPE) block or 15 unstained sections (5 micron). If a lesser amount of tissue is available, contact the sponsor. An archival specimen is acceptable for Phase 1; a de novo specimen is required for Cohorts 2, and 3 if the T790M status was confirmed by tissue biopsy. Partial Exclusion Criteria: For All Phases/Cohorts Previously diagnosed brain metastases, unless the patient has completed the treatment that is clinically indicated, if any, and has recovered from the acute effects of any treatment that was delivered prior to study registration, have discontinued corticosteroid treatment for these metastases prior to registration, and are neurologically stable. Major surgery within 2 weeks prior to registration. Radiation therapy, excluding stereotactic radiosurgery (SRS), within 1 week prior to registration. Systemic anti cancer therapy within 2 weeks or 5 half-lives (whichever is longer) of registration excluding EGFR TKIs. Patients on EGFR TKIs must discontinue the agent for a minimum of: * 2 days prior to registration for erlotinib or afatinib, or 3 days for gefitinib if they will be part of the lead-in single dose PF-06747775 PK study (Phase 1 Dose Escalation Single and Multiple dose PK and ECG Assessments; Phase 1 Sildenafil at MTD; and Phase 1b/2 First-Line Single Agent). Please contact the Sponsor for direction for any other EGFR TKI. * 5 half-lives or 5 days (whichever is longer) prior to registration if they will be starting on continuous PF-06747775 dosing directly (Phase 1 PK sub-studies at RP2D; Phase 1b/2 Combination with Palbociclib; Phase 1b Combination with Avelumab). Partial Exclusions for Cohort 2A and 2B (Palbociclib combo): Prior treatment with a CDK 4/6 inhibitor. Partial Exclusions for Cohort 3 (Avelumab combo): Prior therapy with an anti PD 1, anti PD L1, anti PD L2, anti CD137, or anti cytotoxic T lymphocyte associated antigen 4 (CTLA 4) antibody (including ipilimumab, tremelimumab or any other antibody or drug specifically targeting T cell co stimulation or immune checkpoint pathways). Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent. Patients with diabetes type I, vitiligo, psoriasis, or hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible Use of immunosuppressive medication at time of randomization