Sort of, mostly no.
It's not clear if you're asking if a PGY-2 and PGY-3 currently in training can swap, or if they could plan to swap at the beginning of next year (i.e. they are currently a PGY-1 and PGY-2, and want to swap starting in July 2018). So I'll address both.
From an ACGME and funding standpoint, programs are capped at a maximum number of residents. The exact breakdown of those residents isn't defined, so nothing stops a program from having more PGY-3's and less PGY-2's, or the other way around. So, in that viewpoint, this is possible.
But the problem is what happens next. If one of my PGY-3's was to swap with a PGY-2, my count of residents would be fine this year. But then next year, I'd have one extra resident (the PGY-2 would now be an extra PGY-3, and the PGY-3 who left would have graduated). So now I'm over my cap. This can be addressed -- a program can petition the ACGME for a temporary increase in complement, but they need their institution's approval and it's a bit of a pain to do. This assumes the program is not on probation or other ACGME troubles. And ACGME permission doesn't equate to funding, so that's an issue also.
The next issue is curricular. If you're talking about a "hot swap" -- i.e. you switch now in the middle of the year -- the PGY-2 resident can't take the schedule of the PGY-3 resident. Most programs have specific PGY-3 only rotations. Likewise, the PGY-3 who swaps into the PGY-2 schedule misses the PGY-3 specific curriculum. Perhaps some programs treat PGY-2 and PGY-3 the same, then this isn't an issue. But usually there's medicine consults, "senior in house", or other specific PGY-3 rotations. If you're talking about a July swap, this is less of an issue since the program could build out the appropriate schedules. Still, you end up "short" in one class and "fat" in the other, and this could adversely affect the schedule -- if there is always a PGY-3 on call at night, and you're short a PGY-3, that's extra calls for everyone who is left.
As you mention, this would all need to be acceptable to all parties. So, possible but unlikely would be my assessment.