This article considers a new type of integrated multichannel Transcranial Magnetic Stimulator and Magnetic Resonance Imaging (TMS/MRI) system at 3T that is currently being designed. The system will enable unprecedented spatiotemporal control of the TMS-induced electric fields (Efields) with simultaneous rapid whole-head MRI acquisition to record the brain activity. A critical design question is how TMS coil elements interact with the transmit field B1+ of the volume coil integrated in 3T MRI systems. In general, the TMS coils are not designed to have any resonant characteristics at the MRI frequency, they may potentially disturb the RF field due to the eddy currents induced. This is especially a concern with a multichannel TMS setup where the subject's head will be largely covered with the stimulation coils. Therefore, we investigated this problem by computational simulations with realistic TMS coil geometries and a birdcage transmit coil in conjunction with a human body model. We compared the B1+ interaction effects of a commercially available MR-compatible TMS coil with our coil prototype. In both cases, the results show small local changes in the transmit field B1+ of the birdcage coil. Maximal Average Specific Absorption Rate (SAR) values over 1g tissue were found to be slightly lower when the TMS elements were present. We conclude that it should be feasible and safe to use the conventional body transmit coil even when an array of TMS coils is used.