How can I mask a second domain name for a sub brand?

We want to add a sub brand to a storefront with a main brand. I’ve created a test site, using alternate layout for the second brand and all is great. (client wants two brands, one shopping cart)

My second home page is /pages/brand2.. How do I mask that domain name to be brand2.com? Is that possible?

Thanks in advance.

Kriszti