If you put the library in a place both people can access, such as an external drive, or even just a shared folder on the same disk, that will work. To do that, quit Together if it's running and move the library folder to the new location.

If you want to see where the library folder is, before quitting Together hold on the Command key and click "Together" in the title bar of the window, then select the topmost folder to show that in the Finder. That's the folder you need to move.

Using Together like this won't work so well if you use fast user switching (i.e. you switch to another user without logging out first). You need to quit Together before switching users so that it saves its library. If you don't, Together will show a message that its library may be being used elsewhere, but it's best not to rely on that.