Chordomas

Primary Objective: 1\. To determine objective response rate (ORR) according to RECIST v1.1 of pembrolizumab and high-dose pemetrexed in the treatment of patients with chordoma until disease progression. The OOR will be investigator assessed. Secondary Objectives: 1. To describe the adverse events associated with administering pembrolizumab and high-dose pemetrexed combination treatment. 2. To determine disease control rate based on imaging and overall survival. 3. To determine median PFS and PFS rates at 6, 9, 12, and 18 months. 4. To evaluate changes in volumetric tumor measurements based on imaging. 5. To determine the effects of combination treatment on quality of life, assessed by the EORTC-QLQ-C30 questionnaire. 6. To assess tumor evolution over time in patients with chordoma based on imaging, and molecular profiling. 7. To assess the pharmacodynamic effects of treatment in blood. Exploratory Objective: 1\. To explore the relationship between molecular phenotype and patient response.