You're asking if work can be submitted twice. It can't. Think about it. If something like this could be implemented, then I could take my hashing power and multiply it by connecting to multiple pools. So, in pool 1, I have 1TH/s, and pool 2 I have that same 1TH/s, and in pool N I have my 1TH/s, effectively giving me N TH/s mining, when I only have a single terra hash of hardware. So, to answer your question, no, that kind of pool is not technically feasible to implement.
P2Pool does nothing of the sort. P2Pool has its own block chain called the share chain. Each share that is added to the chain either solves the BTC block or it does not. If it does, the generation transaction includes the payouts to all the miners who have shares on the chain. If it does not solve the block, it is just added to the share chain.
I think you got closest to what I was asking, but not quite.
I did not mean to ask "
if work can be submitted twice" as you say.
When mining directly / solo mining, I assume you still get rewarded for solving part of the chain, however, most solo mining nodes (including this one) do not relay those minute rewards (if any), only IF you solve the entire block. So that was the crust of my question, can a solo mining pool be set up whereby rather than (realistically) mining for nothing short of hitting the jackpot, the mining can be rewarded however lowly?
Thanks for explaining, and I am sure I am missing something that is obvious to yourself (but ofcourse very foreign to me!).