Not sure how you'd do multi-user read status so that it only goes unread after everyone has read it.
One idea that could work with two users: inbox rule that flags each incoming mail. Then the first person will cause the status to be read, but still flagged. If the other user sees the mail as read but flagged then they know they are the second to read it, now manually mark as unflagged.
Or, if your mail client / webmail client supports it, only mark as read manually and only after (while) moving to a 'actioned' folder. TBH anything in the inbox (or 'to be actioned' folder) can be thought of as unread/unprocessed until moved to the 'actioned' folder.
You can also use mail forwarders to send a copy of mail to one or more real accounts. But you will need to liaise to know that the mail has been actioned.
What we have is a personal email for each family member and then a catchall address for any other address that doesn't have its own account on our domain. I've further set up rules that redirect known 'non-account-addresses' to the right person (mostly these will be matching on a per-user 'code' in the email address, e.g. <shopname>
[email protected]), and everything else gets redirected to a home account. This way I can create on-the-fly per-shop/per-website email addresses and still have them in my own inbox, and others in the shared home (e.g. utilities). Any of these that get harvested and heavily abused gets their own forwarder to a junk account.