I don’t use Mastodon, but I don’t know if it’s possible to do this particular combination:

without owning a domain

users on the local server should still be able to follow accounts on other Mastodon servers

Like, a client that supports having accounts on multiple Mastodon servers would work. Then they have a local account, and they have an unrelated account elsewhere on another Mastodon server and follow people using that, so that the “following” has nothing to do with your local server.

But if you want federated behavior, where a user connects to your server and has their account there tell the local Mastodon server to pull down posts from another users somewhere out on another Mastodon server, you might need to have a certificate on your server that other servers recognize as valid, which in practice would mean one signed by a public CA.

I don’t know for certain whether this is actually necessary, but I could believe that it is.