Ask HN: Any system to store personal email archive?

I would like to change my (very well known) e-mail provider, with 8 GB after cleaning. However the other providers I see offer less storage for a good price or more space with more expensive plans.

I would like keep my emails in a personal storage, local or cloud. Allowing me to search, add new emails, synchronize with other accounts (if possible), etc...

Edit: My idea is to change to another email provider and move all archives to a personal system.