Domain Mapping to add another domain

Hello,

Is it possible to use 2 main domains?
I already have plusdeprospectspro.com and a new blog is at newblog.plusdeprospectspro.com

I would like to offer another domain to all my clients. For example: mynewdomain.com
So the new blog would be newblog.mynewdomain.com

Clients could either use newblog.plusdeprospectspro.com or newblog.mynewdomain.com: both would work at the same time.

Thank you for your answer,
Millie