Since the source-code isn’t public yet, I can’t be 100% sure about the implementation; but I guess every public key sends a single message which has a voting-power that could be verified by checking the sortition algorithm for that key.
I’d imagine that the protocol wouldn’t send one message per voting power, wouldn’t make much sense from an efficiency point of view. What could happen, is that a key sends multiple messages (each with the same voting power) voting for different values… that’s not a problem under the assumptions of byzantine thresholds.
Anyway, from a logical point of view I think the implementation wouldn’t matter. If the malicious party want to split the voting power in different votes, it could shard his stake in a lot of addresses and choose to vote with each one to whatever he wants.
Splitting stake or not doing it doesn’t change the voting power of the real owner (due to how the cryptographic sortition is done).