Thanks for your response.

Apologies for the bad explanation, the word 'grouping' may be confusing here. I'm not refering to a pool, but a set of miners that is mining a particularly set of transactions (t1), each inidividual miner in that set aims to find a hash for its own block (no shared rewards, like in pools). The tricky part is when two sets of miners (different sets, that is) find a block; the protocol I'm trying to work on should be able to handle two blocks from two different sets of miners (but not two blocks from the same miners in a specific set). The assumption for now is that two blocks can be valid at the same time within the same cryptocurrency network, as long as they come from different sets (not pools) of miners.