I see no problem with that plan as long as you'll have a total of 9 wires (2 hots to 1 neutral). I've seen some people here call them edison circuits. NEC calls them multiwire branch circuits and where I come from they call them networks.
If you aren't familiar with these types of circuits and the hazards of wiring them incorrectly then don't do it. You would need (12) wires in which case you'd need to derate.
BTW you could fit those in 3/4" EMT.
