Can I connect to a separate neutral (white) wire for my switch/outlet combination?
You must separate the neutrals completely.  Neutrals must be monogamous only with their individual hot.  That is a gravely defective installation.  If any neutral wire breaks, the hots together will overload it.   

No need to untangle the Gordian knot right now, there's a simple workaround.  I once had an installation where I had 5 hots on 2 neutrals. (4 is feasible if two MWBCs are exactly correct, but this was not "exactly correct"!)  As a simple fix, I moved all the hots to one breaker.  This removed the overload issue, and for me since I was in conduit, was a compete solution.  For you, you'll still have neutral current returning on a different cable than hot current, and that needs fixing.  But it'll buy you time. 

If you have one cable with two hots and one neutral, wired like a 120/240V circuit except it splits into multiple branches, that is called a ”multi-wire branch circuit" or MWBC.  If you have an existing one, learn all its tricks and traps.  Please don't create any new ones, as they are obsolete. (they don't play well with GFCI/AFCI) 

GFCI breakers are very good "detectives" for this, they will trip if there is any neutral hanky-panky.  Being in a garage, they would need GFCIs if they were new work.  Fixing wiring defects is not new work.