Yeah, there's only one screen for each storage, and I REALLY hate the limiting space it provides considering the amount of loot you get from a few enemies killed.
Fortunately, there's this-
PlugY The Survival Kit
What this does is it adds unlimited space to your stash, a bigger one page inventory, and a bigger one page Horadric Cube (If you haven't gotten this item yet, you will soon).
Some say this is a cheat, and with the way people can use it, yeah I can see it as a cheat. But this gives you space to save up for all the gems you collect, as well as other socket-items if you have the expansion pack (cause there are over 50 runes and a dozen times more combinations that create unique item runewords).