Study of the CDK4/6 Inhibitor Palbociclib (PD-0332991) in Combination With the PI3K/mTOR Inhibitor Gedatolisib (PF-05212384) for Patients With Advanced Squamous Cell Lung, Pancreatic, Head & Neck and Other Solid Tumors

This research study is studying a combination of drugs as a possible treatment for cancer that might have a specific change in the phosphatidylinositol-3 phosphate (PI3K) pathway.

This research study is an open-label Phase I clinical trial, which tests the safety of an investigational drug or combination of investigational drugs and also tries to define the appropriate dose of the investigational drug(s) to use for further studies. "Investigational" means that the drug is being studied. The FDA (the U.S. Food and Drug Administration) has not approved Palbociclib for the participant specific disease but it has been approved for other uses. The FDA has not approved Gedatolisib alone or in combination with Palbociclb as a treatment option for the participant's disease. In this research study the investigators hope to determine if treatment with Palbociclib and Gedatolisib will be tolerated and will help to shrink or stop the growth of the participant's cancer. Palbociclib is an oral drug which has been shown to stop the cell cycle, which is the way a cell initiates growth. Gedatolisib is thought to work by controlling a series of events directing cell growth and survival. Gedatolisib may work to stop or slow activity within tumor cells. By putting these two drugs together the investigators hope that it will have a greater effect on cancer growth than either drug alone.