Refreshing makefile midway through interpretation

I'm working with a c++ project that someone else wrote, and the makefile is quite convoluted. The only way that I can get a certain dependency to build is by having it build and then using sed to change a portion of the makefile. However, this means running the make command twice. This honestly is the only way to solve the issue and I've been tearing my hair out over it.

Is there any way that I can have make refresh the makefile so that it sees the updated makefile before continuing interpretation?

Example of what needs doing:

.PHONY: target1 target2

target1:
        @sed -i 's/Brian/World/' Makefile
        # At this point, make needs to refresh the contents of the makefile to see the changes made

target2: target1
        @echo "Hello Brian!"
        # After the makefile has been refreshed, this will print "Hello World!"

I would write this with a separate temporary copy of the makefile:

Makefile.world: Makefile
        @sed 's/Brian/World/' $< >$@

target1: Makefile.world
        $(MAKE) -f $<

but if the modification never changes (like this), there's little reason to make it a temporary. Unless you're frequently editing Makefile and want to make sure Makefile.world stays up to date.