Colgada is a Tango move, where the feet of the follower are leader are in the same space and their bodies lean apart from each other in a perfect counterweight. The colgada is relatively modern and part of nuevo Tango.
Most discussions I've heard about leading colgadas suggest that thistechnique decision is one that the follower makes. A leader would be well advised not to try big colgadas with someone whose choice on this matter he is not yet familiar with. Better to try some tiny ones first, earlier in the tanda, to see how she responds naturally. If I find someone leaning out away from me in the shoulders in a tiny colgada, I DEFINITELY will not try a big one with them, and will stick with the smaller stuff. If I find they choose a straight-spine-and-legs, hanging-angle-at-the-shoulders axis as the embrace opens (no self-initiated outward lean of the shoulders) or a "butt-sitting" position (vertical spine, with hanging angle coming from the hips) then I assume bigger colgadas would be safe and fun with this follower.
I could imagine leading experiments to try to get the follower to "butt-sit", but my main concern would be that if we failed to share an understanding of the lead, in the middle of a single-axis turn colgada, it would complicate the dynamic balance between us that is my main task to solve as a leader to keep us safe. It seems easier to me to just gently learn what she will choose to do through experience, then work with that expectation as I initiate the colgada.
Basic Colgadas Compact Colgada
Advanced Seminario on Colgadas Step-Over Colgada
Giros and a Simple Colgada