As hosseinimr93 says, you need the threshold number of seed phrases (so 2 in a 2-of-3 system, or 3 in a 3-of-5 system), and you also need the xpubs from the other cosigners.

There are two ways you can go about this. Some people simply back up all their xpubs together in addition to backing up their seed phrases separately. This isn't a great solution for me, because if someone discovers your xpub back up then they can generate your addresses and spy on your wallet. Although they won't be able to spend any coins, they can derive your addresses, see how many coins you have, watch your transactions, and so on.

The way I go about this is as follows. Alongside each seed phrase back up, I also back up a number of other xpubs, such that recovering the threshold number of back ups is enough to recover the entire wallet, but any one back up does not allow an attacker to spy on my wallet. So, for a 2-of-3 system, my back ups look like this:

Back up 1: Seed A, xpub B
Back up 2: Seed B, xpub C
Back up 3: Seed C, xpub A

As you can see, any two back ups will provide me with two seed phrases, plus the third xpub, while any one back up does not allow an attacker to spy on my wallet.

For a 3-of-5 system, it would look like this:

Back up 1: Seed A, xpub B, xpub C
Back up 2: Seed B, xpub C, xpub D
Back up 3: Seed C, xpub D, xpub E
Back up 4: Seed D, xpub E, xpub A
Back up 5: Seed E, xpub A, xpub B

This has the same result, where any three back ups provides all the necessary information.

Obviously this can be a little complex to set up to ensure you are not mixing up your seed phrases and your xpubs, so if you plan to do this take your time, double check everything, and practice restoring your wallet from your back ups to ensure they are correct.