Bazikonn: Is it possible? Or there could be some conflicts?
As noted, depends on the game. I have both the Steam and GOG version of No Man's Sky installed. They use the same save space, so I just make a copy of it and rename the folder to NMSGOG or NMSSTEAM, depending on which one I'm playing. This may or may not work with other games.
Games that don't have registry entries can probably be installed without issue. Just install them to different folders or even different drives, and you should be fine.
But yeah, depends on the game.
teceem: The first thing I was thinking: Why?
It's way easier to run earlier versions of GOG games then Steam. So, you could run an older version of the GOG game and a current version of the Steam game.