Disturbance rejection for uncertain systems is a longstanding problem of both theoretical and practical importance. In this paper, we propose a novel switching-based Adaptive Feedforward Controller (AFC) to remove a priori information on the sign of the plant transfer function at the frequency of interest (the so-called SPR-like condition), which is an undesirable but inevitable requirement for the existing AFC approaches. A distinctive feature of the work presented herein is improving the transient behavior by adopting a new switching mechanism based on an unnormalized adaptation law. Furthermore, the dimension of the overall controller is kept relatively low regardless of the number of candidate controllers. Boundedness of the trajectory of the closed-loop system and asymptotic zeroing of the output are rigorously proved. The effectiveness of the proposed technique is illustrated by numerical examples.