Fraid not. The breakout box plugs into a single D type connector on the PCB soundcard. The same one that the omni uses. Plus there are driver and software issues too. And the software mixer.
Why do you need so many audio inputs? Surely a small mixer plus the Delta 66+ omni would be enough for most small recording project studios?
I have the Delta 66+omni and a s/blaster Live! for midi/soundfont work and will shortly get a 12 channel soundcraft M series mixer. Enough I/O for me