But, note, if the xmax version has a different name in the custommaps page, you'll lose you character skills and likely quests as well.
Again, make sure to back up your character.
If the xmax version and non-xmax versions have different names, then do this:
With both versions installed, go to My Documents/My Games/Titan Quest Immortal Throne/Custommaps/
You'll see a folder called something like Asylumsmod and another folder called like Asylumsmodxmax
Rename Asylumsmodxmax to bak_Asylumsmodxmax
Rename Asylumsmod to Asylumsmodxmax
Open the folder now named Asylumsmodxmax
Open the subfolder called "database"
Rename Asylumsmod.arz to Asylumsmodxmax.arz
Now, start the game, go play through that part of the quest. Once you get to Babylon, exit the game, backup your character again, then reverse the above steps to resume playing with xmax.