The ~2000 known objects orbiting beyond Neptune have revealed significant insight into the formation and evolution of the solar system. About 100 of these Trans-Neptunian Objects (TNOs) have known companions, with 40 having well characterized orbits, including three TNO multiple systems. Until now, Keplerian orbits have been assumed for all 2-body TNO systems, which until now has been a mostly adequate approximation. The field is poised to make a significant improvement in our knowledge of these systems and their orbital and physical properties by characterizing non-Keplerian effects in TNO binaries. I will discuss how studying existing and new observations with our new non-Keplerian modeling tool, MultiMoon, will allow for significant progress in understanding the shapes and orientations of TNOs. We will include preliminary results on TNO systems of interest.