If you've ever been in a good, locally famous thrift shop, you know how long the lines can be. For all their perks, space is definitely not one of them. I don't think I've ever been in a thrift show with more that three dressing rooms, and really any one with more than two will always surprise me.
If you want to skip the lines, why not put on a leotard? As long as it's not to risque, you can probably get away with wearing it instead of your normal clothes, and trying on clothes on top of it outside the dressing room.
Leotards are form fitting enough that they won't take up too much space on your body, allowing for things to be slipped over them. They also cover enough that you won't be exposing anyone to your nudity, which is the only other way you could try on clothes outside the dressing room. Thrift hack!