It all depends on how the multi-signature wallet has been set up.
In a M of N multi-signature wallet, you need to have M out of the N seed phrases, and the master public keys of N cosigners.
Note that your wallet will probably ask you for N-M master public keys, because the other M master public keys can be derived from the M available seed phrases.
For example, in a 2 of 3 mult-signature wallet, you must have one of the following combinations to recover the wallet.
Seed phrase A, Seed phrase B, Master public key C
Seed phrase A, Seed phrase C, Master public key B
Seed phrase B, Seed phrase C, Master public key A
To recover the wallet first seed phrase: you need its seed phrase plus the master public keys (xpubs) for both the second seed phrase and the third seed phrase
Then to recover the second seed phrase: you need its seed phrase plus the xpubs of the other two seed phrases (first and third in this cases)
Their seed phrase recovery: you need its seed phrase and then the xpubs of the other two seed phrase (first and second in this case)
What do you mean by recovering the first seed phrase and recovering the second seed phrase?
You use the seed phrase(s) to recover the wallet. You don't recover the seed phrase itself.