You sure can! First, install one of the versions of the software normally. Next, run the installer for the other version, and in Step 3, uncheck the box that reads either Do you want to uninstall previous CoffeeCup Shopping Cart Designer Pro versions? or Do you want to uninstall previous CoffeeCup Shopping Cart Designer Basic versions?.

uninstall previous CoffeeCup Shopping Cart Designer

Now you can continue the install process normally, and when you're finished, you'll have both versions installed on your computer.