MuSig is just the aggregation of all signatures in a multisig. My solution for scalability leverages MuSig for transactions where you have a bunch of inputs from different people, went to a single MuSig output held by all of them. A sort of "side-chain" can be started at this point, though it is ephemeral and for bitcoin transactions only, and only exists as long as the MuSig UTXO is not spent - this would be like the regular blockchain but with a very low difficulty that only accepts Proof-of-Works that have a MuSig signature from one of the participants (hence N will be very large).

To settle the transactions, the MuSig will be spent by the users (ideally all of them, but this is a diamond's rough edge I have not polished yet*) and the outputs will go to addresses according to the predefined arrangement.

I'm anticipating that in the distant future, the vast majority of Bitcoin transactions (remember, transactions - you still own your keys) will be settled on this new layer that has nothing to do with Lightning - this is going to be the Layer that makes payment networks like VISA obsolete.