I would say that you will have more and more opportunities available to you just as soon as you get a little more flight time.
Right now, you could probably get an opportunity as an F/O on a Citation or a turboprop; after you get your times up to 1500 or so with 300+ jet or turboprop SIC you should be able to find a position on an aircraft that requires an SIC like a Lear, Falcon, Hawker, etc.
Those are just ballpark numbers, obviously, and you might be able to find a better opportunity earlier. At my old job (Westwind) they would love to find a F/O with an A&P just to do paperwork and wheels/brakes and stuff like that, but they are sticking to 2000tt/500multi/100 jet and they would pass on the A&P certificate before they would pass on the experience.