  In this paper we generalize Dillon's switching method to characterize the
exact $c$-differential uniformity of functions constructed via this method.
More precisely, we modify some PcN/APcN and other functions with known
$c$-differential uniformity in a controllable number of coordinates to render
more such functions. We present several applications of the method in
constructing PcN and APcN functions with respect to all $c\neq 1$. As a
byproduct, we generalize some result of [Y. Wu, N. Li, X. Zeng, {\em New PcN
and APcN functions over finite fields}, Designs Codes Crypt. 89 (2021),
2637--2651]. Computational results rendering functions with low differential
uniformity, as well as, other good cryptographic properties are sprinkled
throughout the paper.
