I don't have as many classes as you, so this may not work for you,
but here is what I do. My portfolios are 18 x 24" paper folded in
half. Each table group then has a tagboard folder that they keep
their portfolios in. The posterboard/ tagboard is color coded and my
tables are labeled by color. Each class has a plastic box ( I have
also used flat boxes that fruit comes in at Costco) that the table
folders go in. Then when class starts, I get out the box, the kids
grab their table folder as they come in, then all their portfolios
are at their table.
I have a cupboard with the shelves set just far apart enough for the
boxes to fit in, and that gives me room to store them- 2 class boxes
to a shelf.