Is there any way that I can host my own email while retaining privacy?

I currently use an online 3rd-party email service, but I would like to eventually move to hosting my own email server, because it would give me complete control over my data and would be a fun project. The problem is that I use seperate usernames for each of my different ‘identities’ online as a privacy measure, and hosting an email account for each of these on the same privately-owned domain name would allow one to easily associate the accounts with one another. Is there any way that I could host my own email while still retaining privacy in this regard? Or perhaps this is simply not possible?

Privacy Galaxy!