Forks that attack two loose pieces can run into most of the same obstacles as forks that include checks on the king. There is no need to catalogue them exhaustively here; once you've found a forking square, the task of loosening it for occupation by your queen generally is the same regardless of whether the fork involves a check, a threat of mate, or an attack on two loose pieces. But here are a few examples of how the familiar problems discussed earlier look in this context.

How many Black pieces are loose in the position on the left? None (setting aside the pawn at e5). Nor does White have any productive checks. But we also want to examine the results of every capture. RxB is the only one White has to consider; it results in RxR. Now how many Black pieces would be loose? Two: both rooks. The problem then becomes the easy one of finding a square—c6—from which White’s queen can attack the rooks simultaneously. Ask what Black’s response to Qc6 would be; might it be possible for one of the rooks to rush to the defense of the other? No, but only because of the placement of some pawns: the b3 pawn prevents either rook from moving to a4, and the e5 pawn prevents Ra8-e8 from being useful. If either pawn were missing, the fork wouldn't work.

That's one lesson of this problem: the importance, as we have seen elsewhere, of considering whether one forked piece can move to protect the other. The other lesson is that a single exchange—here, 1. RxB, RxR—can radically change the board; in this case it moved Black from having no loose pieces to having two of them.