How to improve the clarity of hierarchical taxonomy terms in edit forms?
One way you could approach this is to use select boxes with an 'add more items' button.

I use Simple Hierarchical Select for single value selections in a taxonomy with levels, but there's no reason you can't use it for multiple selections.

If that module doesn't make an 'add more items' button pop up then put the field in a Field Collection, yes even by itself.  I know for a fact that you can have multiples of those.