I've a single signature wallet but I heard recently that the multi-signature wallet has more security and that interests me as my stored assets increases.
However, I want to know if I'd be needing to create a fresh wallet, getting new seed phases then move assets to the new wallet Or there's a way I could upgrade to multi-signature using the former wallet.
You have to keep in mind that higher the wallet security, the higher the responsibility is.
If you create a standard wallet, you'll make yourself totally dependent on that particular seed phrase, so, your concern will be to maximally secure your seeds, to hide it in a perfect place. You should store your seed phrase on indestructible plate or write it down on paper (not good idea) or on something else more secure and save it in solid metal capsule. I give you this advice because you need your seed phrases to survive in extreme conditions, including earthquakes, heavy fire, heavy rain and so on.
You can also copy your seed phrases and have a two same copies, two storage. But you should always keep in mind that no one should have an access to them, otherwise your coins will get lost.
Now I want to say something about Multisig, since it seems a better option for you. Yeah, it's true that in case of 2-3 multisig, if you lose one part of seeds or if someone steals one part of seeds, you'll still be able to fully recover your wallet but you have to keep in mind that you should save their seed phrases in three different locations and as always, it's a good idea to have a backup of them, you should have a back up of at least two of them. Now you have to find five secure place to store seeds + you have to buy five indestructible plate or solid metal capsule.
Multisig offers better security but the responsibility is so high that I think standard wallet will be a better option.
It's easier to take care of one wife/kid instead of three