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We extend a recently developed algorithm that expands the time-varying parameters onto a single set of basis functions, to multiple sets of basis functions. This feature allows the capability to capture many different dynamics that may be inherent in the system. A single set of basis functions that has its own unique characteristics can best capture dynamics of the system that have similar features. Therefore, for systems that have multiple dynamics, the use of a single set of basis functions may not be adequate. Computer simulation examples do indeed show the benefit of using multiple sets of basis functions over the single set of basis functions for cases with many switching dynamics. Moreover, the proposed method remains accurate even under significant noise contamination. Application of the proposed approach to blood pressure data likewise indicate better tracking capability of the two sets of basis function than the recursive least squares or a single set of basis functions.