The Kepler Space Telescope found over 700 systems with multiple transiting planets during its prime mission. These “Kepler multis” are the most information rich and dynamically interesting set of exoplanetary systems. About 200 of these systems have one or more planets with a nonlinear ephemeris (Transit Timing Variations, TTVs) produced by interactions between planets. We selected 46 Kepler multis where one planet showed clear TTVs that were not obviously caused by the other known planets. Using the PhoDyMM photodynamical modeling tool, we explored the systems’ physical and orbital parameters with an n-body integrator that calculates a model lightcurve coupled with a Bayesian Markov Chain Monte Carlo algorithm. We first examined if different configurations of only the known planets could cause the observed TTVs. We then predicted possible additional planets and performed the same analysis creating new models. The majority of the systems in this study show a significant preference to a model with an added hidden planet. This analysis gives us preliminary parameters for over 30 possible new planets as well as giving us insight into the structure and dynamics of these systems.