Can I have two separate business contact databases open at the same time? If
yes, how do you create a second one without losing the first one?

When you create a second db, the first db is disconnected from your
Mail profile, but it is not deleting, its files remain on the disk and
attached to the sql instance. You can then switch back to it.

Or you can can create a second Mail profile and have each profile
connected to a different database.