There Are Other Ways to File Your Paper
Pile with dividers. If you pile with intention and understanding of your system, then using file folders to divide your stack can help you identify where one "project" begins and another ends. You can also use clip on tabs to identify the section. There are products available at your local office supply store that are made for piling. Remember though, maintenance of your system is still required.
Stack with sorters. Using a literature or document sorter to organize your files is a great way to go vertical and still see your categories. As with all systems, establish a maintenance routine to keep it in order.
Sort and store with drawers. If you have the space for those towers of plastic drawers, they may be perfect for projects or larger categories. The drawers provide easy access and a built in maintenance reminder (if you can't close the drawer — it's time to go through it). And if you are a visual person, the clear drawer fronts provide a quick view of what's inside in addition to the label.