It's called HYLLIS, it's dirt-cheap and it's awesome.

Space for four keyboards (to put on display) but easily extendable with some tools.
If you're just looking for a storage solution in your basement, you can probably stack up to six Cherry boxes on each level!
I've got four of those bad boys (only one for displaying) and so far I'm more than happy with them!
How to expand HYLLIS:
So far I've come up with two ideas.
1) Pretty straight forward and probably the cleanest solution: Buy a second (or even third) HYLLIS, drill some holes and screw the floors into one of them.
2) This one is more artistic and just for displaying: Get some wires/cords or whatever and tie them with enough space around the floors. This way you can mount three more keyboards.
Here's a visualisation:

So, yeah. Now you know what to do next weekend. Just don't bring your wife/girlfriend or it might get expensive after all.