Domain mapping and Subdirectory site Unity

I have a website where I intend building landing pages for a few business . i have an issue that i need help with. let's assume root website is. http://www.abc.com and a business registers on the site as xyz.

the the url of that business will be http://www.abc.com/xyz.

Then a user decides to map a domain xyz.com to http://www.abc.com/xyz.

i want any visitor to be able to access the same site using urls abc.com/xyz and xyz.com without any redirection is this possible. Is this possible and how can I go about this.? Your support is most appreciated