Generating the keys separately and they would work normally?
Wonders shall never end, here I am thinking I've known what's needed to know.
I hope I have understood your question correctly. What you perhaps may want to read is about the P2(W)SH methods to build transactions, which is the way multisig are built (P2TR - Taproot - also works but P2TR has some challenges to make it "more secure" than a regular single-signature P2(W)PKH transaction due to the so-called "key path").
As you probably know, the receiver of a Bitcoin transaction has to solve a mathematical challenge. The challenge for a regular P2(W)PKH tx is: "Provide the public Key corresponding to the address I stored in the transaction and then sign the coins with the private key associated with this public key".
In the case of P2WSH or the older P2SH, the challenge is different: "Provide a script which corresponds to the hash I stored in the transaction. If the script contains public keys, provide signatures for all private keys associated with it." (this is very simplified, there are also other kinds of scripts possible)
All these keys can be generated in the way you want, so you can use several different entropy sources (e.g. different Bitcoin wallet software) if you want -- you only have to be able to build the script, and then provide the hash of the script. And of course you need to know store the private keys somewhere (offline preferrably).
The nice effect Charles-Tim described is that the "redeem script" is not visible until the coins are spent. A hacker only sees there is a P2WSH transaction, he can't see if it's a multisig or some other kind of contract.