Yes - This is a common requirement that can be accommodated by opening the Person's record > Scrolling across the list of tabs at the top of the screen to access the Contact Details tab > Click New Contact Details and add the new additional address.

Any emails sent to or received from the Person's email address, or any email addresses listed in the additional Contact Details, will be listed in the Person's Emails tab.

As above, using multiple contact details enable you to record different address and/or telephone and/or email details for a Person or Organisation.  In addition, a really useful application of this is if a Person leaves one employer and moves to another.

The likelihood is that you'll still want to see the history of emails you exchanged with that Person.  Emails are attached to a Person if the email address on the Person record matches that used on the email.  If you change the email address on the Main tab of a Person record, the emails sent to the previous address will 'disappear' from the Emails tab.  So, if you want to keep all the emails that were exchanged when using the previous email address, simply create a a new set of Contact Details (calling it Old Employer, or something similar) and enter the old email address in the email field.  Now the Emails tab will show all the old emails as well as any exchanged using the new address.

You can use the same technique if you start corresponding with someone using a personal email address and then they provide a work email address.

NOTE: Since an update earlier this year you now also have alternate phone number and email address fields present within these records. You can reveal them by creating a custom page layout.