What game are we talking about here?
Most games won't install a second time as long as their original registry entries are still intact.
What you could do is simply install the game once, as normal, to whatever directory you choose. Once the game is installed, copy, not move, the entire folder containing the game to a second location. Depending on the game, the game may still work, or it may not. If it doesn't, just delete the copied folder. If it does work, then add your mods to one of them. Then, locate the executable of the copied version and create a shortcut on your desktop or wherever you choose (so you don't have to go through the folders each time to start it).
If that doesn't work (because of registry issues), there's a longer route you can take, which is much the same, but will require TWO extra copied locations, and means you have to overwrite the game every time you wish to use (or not use) the mods.
Location 1: Original installation folder.
Location 2: Backup of original installation folder.
Location 3: Modded copy of game.
When you want to use the mods, copy the modded folder over the original installation folder. When you want to switch back, copy the original backup over the original installation folder. Depending on the size of the game's installed files, this could take a while. Alternatively, you could backup and copy only the modded files, if you know exactly what they are and where they go. Using this method, you are still using the original installation folder, so the registry shouldn't give you any issues.