I've tried to change the titleid (the id that is checked when trying to install a game to see if you have it installed already) and it worked for Mario Kart 7. It did not work when I tried it with multiple different roms for Alpha Sapphire.
Edit: Just to clarify, both games I mentioned installed side by side with the originals. Mario Kart ran properly, but Alpha Sapphire wouldn't run (black screen after starting it).