Is it possible to redirect an HTTP client "behind the scenes" (domain name in URL in browser does not change)?

Is it possible to redirect an HTTP client "behind the scenes" (such that the domain name in URL in browser does not change)?

 

 

For example, if the client browses to ...

 

 

http://www.vanityname.mycompany.com/

 

 

... we want to redirect them to ...

 

 

http://www.someothercompany.com/vanityname

 

 

... but we don't want the client to see the hostname change from www.vanityname.mycompany.com to www.someothercompany.com.

 

 

Any help or guidance will be most appreciated.

 

 

Thank you.