Anti-CTLA4 takes the brakes off the immune system to allow otherwise hidden immune responses to become more active. In so doing, there could be other side effects, such as immune system attacks against the normal organs of the body. We will follow both the anti-tumor immune responses with frequent blood tests and follow and treat side effects people develop on this study to determine if anti-CTLA4 is worth pursuing in a larger number of patients with synovial sarcoma or other sarcomas.