Remove Crossing branches and trunks

Remove tie

Perform Crown Raising (vista pruning)

we can not give pruning advice ... unless you untie it.. and let us see what we are supposed to be fixing ... eh???

you never tie up a tree/shrub as you tried ... you use pruning to shape it the way you wish ...

i am not personally involved with this plant.. so i would start with pix of specimens.. such as at the link ...

the key here will be.. WHATS YOUR GOAL ... if you can ID that.. then you can figure out how to prune ....

ken

https://www.google.com/search?q=Anacacho+Orchid+Tree&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiQzpqSl5nPAhWNpYMKHYKtD70Q_AUICigD&biw=958&bih=745&dpr=0.9

but do understand.. with your goal ... and with trees ... its all in tree time.. which means you may be pruning on this things for 5 to 10 years ... before you achieve your goal ... i call that.. tree time ...

with the caveat that.. you can always cut more off next year.. but you cant glue them back on ... lol...

ken

I agree with ken. Unless you want to plait it, get rid of the tie. The way the stems are growing does make me wonder. Is the wood flexible? Maybe you could plait it.

I hadn't come across this tree so I looked it up. Bauhinia lunarioides is a small tree which can be either single or multiple trunked, so yours looks as if it is just doing what comes naturally. If you are happy for it to be multi trunked I'd just remove the ties and leave it alone. If you want a single trunk you'd need to select a main stem and remove all the others. Your call.

Alright, Thanks for all the advice! I am happy with the multi-trunk look, but I'll go ahead and just prune away the crossing limbs. The largest trunk bifurcates into two equal sized limbs that immediately disperse from the tree slightly less than horizontal. If I pruned this trunk below this bifurcation, could I expect the trunk to recover and sprout a structurally sound limb? I suppose this would be somewhat equivalent to tree-topping, which I have heard nothing but badness about, but I don't know how else to approach this trunk.

I would follow floral's suggestions.

Can you remove the ties, give it a day or two to settle and then show us some more pictures? All the time it is trussed up like that we can't see what the branches are doing.

Well, we don't seem to be progressing in understanding what's going on with your tree. As I said earlier, it's hard to get a good overall picture from only the pictures you gave. And, as others have said, it's hard to know what's going on with the trunks all tied up like that. Give us something to work with and maybe we can give you better advice. My gut feeling is that I would likely remove the trunk with the rubbing branches (after all, rubbing branches are not good things!), but without more info, it's hard to know for sure. From looking at the second picture I even wonder if it would be possible to untangle the branches to prevent rubbing.

Sorry for the delay in responding, and thanks for the input. I tried to untangle the rubbing trunks, but was unsucessful, so I did remove it (but only to the point at which the rubbing occurs. Should I just complete the cut all the way to ground level, or could I expect new (healthy) branching from this trunk?

If the rubbing trunk wasn't attached to the other than you should cut it at the base.