You can install 10.7 or earlier version of 10.8 on any partition you like. The difficulty is in obtaining an earlier version, if you haven't saved one yourself.
I find it hard to believe that some software is not compatible with 10.8.5, but compatible with earlier version of 10.8.x.
Point updates are bug fixes, not changes to APIs and architectures.
If you have recently purchased some software that doesn't work with 10.8, I would ask for your money back.