This is a Phase 1, open-label, single center, randomized study to assess the safety and tolerability of 3 different dose regimens of entinostat in combination with pembrolizumab in patients with advanced solid tumors who previously completed Study SNDX-275-0140 (NCT02897778). Up to 30 patients will be randomized in a 1:1:1 fashion to one of three arms. In the event that greater than or equal to 2 out of the first 6 patients randomized experience a dose-limiting toxicity, the next patient randomized to that Arm will receive treatment at a reduced starting dose as outlined in the protocol.