It will depend a lot on the agent. I was on a PHX-LAS flight on a friday night in October that was oversold by five thanks to weather issues in LAS earlier and flights being diverted to phoenix. Since my final destination was EWR anyway, I was happy to volunteer as long as I didn't get in too much later. I pulled out my laptop (^ for free wifi in PHX) and suggested an HP PHX-PIT and a CO PIT-EWR. (The first US PIT-EWR was several hours later.) The GA was happy to do it.

On the other hand I have volunteered other times and suggested routings on other airlines and been told it had to be HP only. So I would say go ahead and try suggesting other routings but don't be surprised if they say no.