Q.How Do I Save A Butterfly Bush Badly Damaged By Snow?
I live in a townhouse complex on a corner lot and the snow removal crew piled all the snow from the parking lot up over the curb. I thought I planted them far enough away from the curb but the plow keeps pushing the pile back at the base to make room for more snow forcing the heap deeper into my property. Not only are my butterfly bushes being shoved over in the process but all the snow is piled on top causing the branches to splay out, break in multiple places and even splitting at the base.
The winter is just starting and there will be plenty more snow here in NJ. The branches are hollow and some are as long as 3ft others are broken all the way down to the soil. Obviously I should transplant it but what can I do now? I have removed the damaged branches by cutting just above the next healthy node. Tying it up would help but I don’t think it will prevent longer branches from getting caught by the snow and causing further damage. I’m afraid to cut it anymore. The ground is soft at this time so a transplant would be possible if advisable.

Certified GKH Gardening Expert
You can go ahead and prune back all the branches and pile 3 to 4 inches of mulch on top. Butterfly bushes bloom on new wood and it will regrow from the roots, so there isn't any need to save the old branches. Then in the spring before the new growth starts you can transplant it to a new sunny area, if desired.
https://www.gardeningknowhow.com/ornamental/shrubs/butterfly-bush/overwinter-a-butterfly-bush.htm