In this paper, a simple and efficient method to enforce nodes, or points of zero vibration, on an arbitrarily supported rectangular plate subjected to multiple harmonics with distinct excitation frequencies is developed. This vibration suppression is achieved by attaching a chain of properly tuned oscillators, configured in series, to the host plate. The governing equations of the combined system are first obtained using the assumed-modes method. Enforcing the node conditions for the given excitation frequencies, a set of constraint equations are formulated, from which the sprung mass parameters can be determined. Two special cases are considered: when the attachment and node locations coincide (or collocated) and when they do not (or non-collocated). For the former case, determining the required oscillator parameters requires one to solve an inverse eigenvalue problem, and for the latter case, it requires one to use a generic optimization algorithm. Procedures to tune the parameters of the oscillator chains are outlined in detail, and numerical experiments validate the proposed method of enforcing nodes to mitigate excess vibration when the plate is subjected to multiple harmonic excitations.