I have two units in base, and my opponent has two units in base. My opponent casts Star Crossed targeting one of my units and one of theirs. I cast Rebuttal and take control of Star Crossed. Can I essentially bounce two of their units back by only reselecting, switching the target on my friend unit to their other unit?

No — when you gain control of Star-Crossed, "friendly" and "enemy" re-anchor to you as the new controller, so you still must choose one of your own units and one of your opponent's.

You may make new choices and can switch either target (e.g., bounce your other unit and your opponent's other unit), but both mandatory targets must be legal relative to the spell's current controller — that's you. One target has to be a unit you control (Rule 740.1), so you can never make both targets your opponent's units.

If you decline to retarget, the original targets stay and the spell just resolves normally: one of your units and one of theirs each return to their owner's hand — a trade, not a two-for-one.