Depends....
You COULD do this if you are talking just changing pins for multiple shots at the same time of day, but here's your problem....
You worry about cross-contamination of your product. If you're shooting 2 cc of substance X and it comes in 2 cc ampules, no problem. If you're shooting 2 cc but have it coming from a 10 cc vial, you risk putting something foreign into the bottle when you make your second draw. The impact it could have on the gear is uncertain at best.
Also, you couldn't do it for drawing then shooting substance X then going to substance Y. Same problem.
It's just easier to have plenty of syringes for your injection needs.