Hello,
There are many ways to make a collapsable vocal booth, and here is the way I acheived it - over a stair well:
https://homerecording.com/bbs/showthread.php?threadid=53631&highlight=flip+floor.
Basically, the floor flips up allowing the stairwell to be used, and flips down for recording. Nothing magical here.
Another option assuming you seek a permanent structure, is to build a vocal booth against the wall, but hinge the four corners so you can "fold it flat" against the wall. Of course you need a flat wall without windows, but thats another option. Picture a sideways murphy bed if you remember those things.
You could also buy/build partitions and stand them up for vocal recording, then pack them flat in an attic or garage when not in use. I've seen that method done a lot and it works fairly well. Very well actually. Its not totally soundproof of course, but its totally collapsable and you can set it up anywhere you want pretty easily.
Another option is to build or purchase a vocal booth, from a company like
www.vocalbooth.com, and mount it on casters. While not collapsable, if its installed, say, in your garage, you could disconnect the wires and push it aside or towards the back of the garage.
There are a lot of ways to solve this need, and I hope I gave you a good starting point.
And egg cartons as compared to acoustical foam is to be considered useless.
