Focus on the squeeze against yourself
Any squeeze with three menaces, and some with two, will have two or more menaces in one hand. Almost always, we will need to squeeze that hand. The crux of most of the more advanced squeezes is how we time that. Consider this delicate layout:
We will eventually, perhaps immediately, play two clubs and we have nothing in dummy we would like to give up. Normally with two menaces (or two stoppers), such as the major suits in dummy, we are squeezed on the last winner outside those two suits (that is, the last minor-suit winner). However, the ♦5 is playing an important role as well: it is the Tic in the Last Strong TicKet. In effect dummy has 2.5 menaces and will be squeezed on the last winner outside its menace suits, that is, the last club.
Consider the West hand: it has stoppers in the pointed suits and so will be squeezed on the last round-suit winner. Two clubs right now will pose no problem to this hand.
If we squeeze dummy before West, we will squander a needed threat. West will not be squeezed while the ♥A is outstanding, so we must play that card. Only then do we play our two clubs. Dummy will still be squeezed on this trick, but only after West.
When we do squeeze our busy hand, we of course need to pitch carefully. The general rule is to keep what second hand discards and pitch what they keep. In this case, West will normally keep spades and pitch a diamond. Thank the ♠2 for its important service, and discard it.