Assuming that the dancers haven't made a mistake that kills symmetry, and if you can get to a normal (every boy has a girl on his right) 8 chain through setup, you can resolve the square, no mater who is with who.
If before steps 1 or 2 below, you notice that everyone is facing his corner (assuming that 1 and 4 are your primary and secondary couples, for example, boy 1 is facing girl 4, and boy 4 is NOT facing girl 1), you in or close to a corner box. If the outsides don't have their partner, do a right and left thru. Then, either way, you are in a corner box, so skip to step 5.
If before steps 1 or 2 below (and you are in an 8 chain thru setup rather than temporarily in something else), you notice that everyone is facing their partner (that is, your key couples are each facing their partner), skip to step 4.
1. (After checking for facing partners/corners for short cuts above) pick out your primary couple (for most of us, couple 1). If, and only if, they are either both centers or both ends, do one only of flutter wheel or reverse flutter or two ladies chain. Then, either way, move on to the next step.
2. (After first checking for facing partners/corners for short cuts above) pass to the center.
3. (You are not in an 8 chain thru setup at the moment, no need to check for facing partners/corners.) The man of one of the key couples is in the center. His partner is either in the same box that he's in (behind him and to his right, call this bs for boy same) or the other box (facing him with one girl between them, call it bo for boy other). Similarly, the girl of the other key couple is in the center. Her partner is either in the same box (call it gs, he is behind her an to her left) or he's in the other box (call it go, he's facing her with another boy between them). There are 4 possibilities:
bo, go: Centers pass thru
bs, gs: Centers square thru three (Of course this means that you missed noticing that everyone was facing their partner before step 2. If you take the shortcut, we never get here.)
bo, gs: Centers two ladies chain (or reverse flutter); then pass thru
bs.go: Centers flutter wheel; then pass thru
(Except for bs, gs, which shouldn't happen, we're making a call to get to state bo, go and then passing thru.)
4. (Now all are facing their partner, which is why you come to this step if you recognize this state before steps 1 or 2.) If whichever key man is on the outside is standing next to his corner (boy 1 with girl 4, or boy 4 with NOT girl 1) square thru 3; otherwise, pass thru.
5. Left allemande, promenade home (or equivalent).
Note 1: Only slight modifications are needed to work from double pass through setup
This is the configuration for step 3, except that you might have both members of a couple (say couple 1) as centers, or both as ends, such as would have caused you to flutter wheel, etc. in step one. You can fix it here by calling either of girls zoom or boys zoom (but not both). Continue from step 3, except that bs, gs is quite possible, and you must recognize it and remember that it requires square thru 3.
Note 2: To go from completed double pass thru, Do a cloverleaf, or all partner trade, then continue as for double pass thru setup. One option is to have teh girls or the boys zoom before hand, though waiting until after may give better success (not sure). Another possibility for plus and above is track 2, then if both members of a couple are facing in or both facing out, girls trade (equivalend to ladies chain in the original step 1), and hope that they know how to pass to the center from a wave, or make step 2 be step through, outsides trade.
Note 3: From a trade by setup, trade by, then go to step 1.
Note 4: From general columns, circulate (or magic circulate) as necessary so that every boy has a girl. From right handed columns, boys run. From left handed columns, girls run. From magic column, pick someone to run and tehn fix any half sashayed couples (centers or ends, but not both). You now have either an 8 chain thru setup, or something handeled by the notes above.
Note 5: From facing lines, touch 1/4, then proceed as in note 4.
Note 6: From two faced lines, wheel and deal, then step 1.
Note 7: From inverted lines things like centers pass thru or ends pass thru and bend the line will give lines facing, proceed as in note 5.
Note 8: From 3 and 1 lines, cycle and wheel, if in level. Else outfacers uturn back, or odd person run, if then facing out, bend the line, continue as in note 5.
I fyou have T-bones, you're on your own.