To do it on Mac, install one copy (by default it goes to /Applications/Diablo II). After the installation has finished, rename this directory to something else - for example, call it "Diablo II Key 1".
Then proceed to install your next copy (to /Applications/Diablo II). After the install, rename it again (eg. "Diablo II Key 2"). This way you should be able to keep track of what's what.
Once two copies are installed, just run each application. There are no tricks to it.