Make pattern matching question

[rsheridan6]

Hi,

I have some targets with prerequisites of the form [target][some
variable text].[extension-name], where there are several extension
names.  I'm trying to make a static rule to do this, but I can't make
it work.  I've tried this (among many other things):
$(EGGS): %: $(wildcard %*)
    do-stuff-to $^

I didn't get far enough to try to filter the extensions I want, I'm
just trying to get the equivalent of bash's "ls %*" where % means the
target name.  Is this possible?

Thanks for reading this far.