I live with my partner, and we would like to have a single "filing system" that allows us both to access our mail.

Unfortunately, it is not yet possible to set up a shared repository with access permissions accessible with different logins. You can only access your data from different devices with one login. This works if you have e.g., 2 mobile phones. So, you always can see the same folder and mail on both.

However, what you can do is to scan the mail of several people from one household. You can find more information on setting this up here.