Standard multi-signature transaction BitcoinCore
Bitcoin Core will be default only treat M-of-N multisignature outputs as "yours" (contributing to your balance) if you own private keys to all N public keys. This is to prevent showing something as a balance which could be spent from under you.

If you instead of using a raw multisig output use P2SH the same rule applies, but in that case you're able to use importaddress to mark the outputs as yours regardless of whether you have access to the keys.

Once the outputs are treated as yours, you can use signrawtransaction to fully or partially sign for them.