makefile with computed variables inside a search pattern

I am working on a makefile that I think should use computed variables inside of a pattern. As part of a larger project I have three different parsers that have a lot of overlap and are written in modular form so as to be able to maintain the common components more easily. The relevant part of the makefile is this:

parser1object = firstobject
parser2object = secondobject
parser3object = thirdobject


$(srcdir)/HIG%.y: \
    $(srcdir)/HIG%.y.1 \
    $(srcdir)/common.tokens \
    $(srcdir)/HIG%.y.2   \
    $(srcdir)/common.syntax  \
    $(srcdir)/HIG%.y.3
sed 's/parserObjects/S((S*)object))/g' \
         $(srcdir)/HIG$*.y.2        >$*temp.tmp
sed 's/parserObjects/S((S*)object))/g' \
         $(srcdir)/common.syntax >common.syntax.tmp
cat $(srcdir)/HIG$*.y.1 \
    $(srcdir)/common.tokens  \
    $*temp.tmp common.syntax.tmp \
    $(srcdir)/HIG$*.y.3 >$(srcdir)/HIG$*.y
rm -f $*temp.tmp
rm -f common.syntax.tmp

That is, I want to concatenate a number of files into one of several grammar files for bison. In the common syntax file I have some references to a generic object that need to be replaced with the name of the object in the respective parser. However, because it is inside of a pattern, the variable replacement mechanism doesn't seem to work as I had hoped. (For parser1, I want to change $($*)object to $(parser1object) and finally to firstobject.

How can I achieve what I want to do?

Incidentally, because of the pattern replacement this seems to be different from {Makefile and computed variable names}