There is no limit to the amount of items you can process in a 3x3 chamber, but there is a limit to the amount of items that the interface will insert. If you put a Steve's Factory Manager Item Valve underneath the chamber and hook it up to an Inventory Controller and a couple of buttons for in and out, it can insert the items and extract them without opening the chamber walls and bypassing the capacity check. It's a little bit hugely cheaty, but it does the job.
The first version I built used a hopper, which I broke and moved to insert and extract when I wanted, that was the proof of concept, then I switched it over to a proper SFM control system. You could also use item ducts and levers to control the insert and extract, with the Item Valve being the only SFM block required.
Upgrading might still be worthwhile, though, as it increases the air capacity in the chamber and so the pressure will last longer.