Schwine1
You can archive those emails you particularly want to keep.
Whether IMAP or POP, you can create a mailbox " on my Mac" called,say, Archive.
Then move or copy, as you will, those emails you have received or sent to the Archive mailbox.
It's unlikely you would want to store every email received or sent, so you can be selective.
Or you can set up rules to move emails to Archive according to criteria determined by you.
Ian