GNU Parallel running Makefiles with different optimization levels

There is not a optimal -O level. My approach in order to find the fastest execution for my particular code is to compile the same code with usual optimization levels (i.e. -O0, -Ofast, -O1, -O2, -O3,-march=native) and check which flags produce me the fastest execution (with time).

So, there is a way to check all optimization levels (listed before) running a Makefile with each optimization (-O level)?

I think that Gnu Parallel could run the Makefile changing the -O level but I don't know how figure it out?

Thanks in advance.