Vibratory power flow through a nonlinear path into a multiresonant support structure is considered via an example case, a hydraulic engine mount. System equations for the nonlinear source--path--receiver system are developed for periodic excitation and an efficient solution method is formulated for the calculation of the steady-state stable response based on a multiterm harmonic balance approach with condensation and continuation. In this study it is shown that while modeling the isolation path with a ``softened,'' nonlinear expression may only moderately alter the predicted system behavior at the excitation harmonic, it can significantly alter it at higher harmonics. With respect to isolation performance, studies of multiharmonic motion and power transmission show that audible structure-borne noise may be generated from subaudio frequency excitations due to path nonlinearities. It is also shown that support base (receiver) dynamics can significantly affect the isolation performance. For instance, with a multidegree-of-freedom base model, significant levels of vibratory energy at higher harmonics of the excitation are transmitted, especially when superharmonics coincide with receiver resonances.