IMAP proxy

[Gandalf Corvotempesta]

I'm migrating an old server to another old server (same dovecot
version in both servers)
The migration itself is straightforward, stop dovecot on the old
server, migrate everything via rsync, start dovecot to the new server.

There is only one step left: change the dns configuration, pointing
from the old server to the newer one.
As most of domains are not managed by me and some other domains are
pointing to our server via IP, I can't simply change the A record or
wait for all users to change their domain configuration.

TL;DR: is possible to use dovecot as IMAP proxy so that even after
changing our dns records, any user directly connecting to my old
server would be proxied to the newer one automatically ?

Any additional software or only a configuration change is required ?