Yes, it's possible, I did this with mine.
For it to work and look correct, you'll need to buy:
- Logic board
- CPU(s)
- Northbridge heatsink
- CPU heatsinks
- Front fan assembly
- RAM risers
- Memory cage
- CPU cover
- Wiring harness
You don't need a new PSU, but you'll need to modify the connectors so they plug together.
You may not need to buy a new wiring harness, as I believe you can modify the existing one, but I didn't attempt it.
You will need to remove the stand-offs used for the memory cage as they are in the wrong place for a 3,1.
Other than that, it's just like giant lego.
If you're not bothered about it looking right internally, I think you can get away without buying the CPU cover and front fan assembly.
I had to buy a new front panel, but I'm not sure if that's essential.
Also, make sure you get a decent 3,1 logic board. I went through 3 before I found one that didn't light up with errors on the diagnostics LEDs.
Edit: It was a lot cheaper than buying a 3,1.