A power mode approach to estimating the vibrational power transmitted to a receiver structure by multiple sources is reviewed. This approach is then extended to estimating the power transmitted to a flexible receiver from a stiff source through discrete couplings. There may be both translational and rotational coupling degrees of freedoms, and/or force and moment excitations. Approximations are developed for the upper and lower bounds and the frequency average of the transmitted power. These depend only on the point mobilities of the source and receiver, and thus require much less data than an exact description. The approximations are most accurate when the mobility or stiffness mismatch of the coupled system is large enough, e.g., the source has, on average, low mobility compared to that of the receiver. Numerical examples are presented concerning a multi-point coupled beam/plate model.