The purpose of this study is to evaluate investigational treatments (study drug) for locally advanced or metastatic solid tumors with oncogene amplifications to determine if any of these study treatments improve overall survival as compared to standard treatments.

The goal is to determine the optimal dose level, safety, and tolerability for the study drug BBI-355. This is the first study to test the study medicine BBI-355 in humans; BBI-355 is not FDA approved by the U.S. Food and Drug Administration (FDA). Treatment for this study may be up to 3 years. The procedures include taking study drug orally, blood and urine samples, diary entries, and CT scans. Risks include diarrhea, nausea, vomiting, fatigue, muscle weakness, dizziness, and headaches. You may or may not receive a direct benefit from participating in this trial, however, information learned from the trial may help other people in the future.

This study is for patients that have been diagnosed with Merkle Cell Carcinoma. The investigational drug in this study is pembrolizumab. The purpose of this study is to compare the usual approach of post-surgery observation with or without radiation to using pembrolizumab with or without radiation after surgery. Participants can expect to be on this study for a total of 5 years.