The Kepler Space Telescope found over 700 systems with multiple transiting planets during its prime mission. These multi systems 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 multi systems where one planet showed clear TTVs not obviously caused by the other known planets. We analyzed these systems with the PhoDyMM photodynamical modeling tool to explore their 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 tried models using different configurations of the known planets to determine if they could reasonably cause the known TTVs. We then predicted possible additional planets and performed the same analysis creating new models. A few of the systems studied produced good results with the known planets but the majority required the addition of an unseen planet. These new models give us insight into the structure and dynamics of these systems as well as putting forth the locations of several possible new exoplanets.