During its prime mission, photometric brightness measurements from the Kepler Space Telescope revealed over 700 systems with more than one transiting planet. Kepler's multiple transiting planet systems (multis) are the most information rich and dynamically interesting set of exoplanetary systems. Dynamical interactions between planets can be observed in about 200 of these systems as small shifts in phase so that the transits do not follow a perfectly linear ephemeris. These deviations from a periodic set of transits are known as Transit Timing Variations (TTVs). We picked 46 multi systems where one planet had a clear TTV that did not appear to be caused by the other known planets. We analyzed the systems using the PhoDyMM photodynamical modeling tool which explores physical and orbital parameters through an n-body integrator that is used directly to calculate a model lightcurve coupled with a Bayesian Markov Chain Monte Carlo algorithm. We first tried to determine if the TTVs could reasonably be explained by the known planets. For all systems, we then predicted possible additional non-transiting (and heretofore unknown) planets and created new models. A few of the systems’ TTVs could be ascribed to the known planets but the majority required an unknown planet to produce a good model. These new models provide strong insight into the structure of these systems as well as the locations of several possible new exoplanets.