I want to redirect the user to a URL that will actually be exactly the same
URL on the same site, but with a different Domain.

For example, let's say the page where the user currently resides is
  http://DomainA.com/SomeFolder/Default.aspx

and I want to redirect the user automatically to whatever their current path
is on the site, but with a different domain:
  http://DomainB.com/SomeFolder/Default.aspx

DomainA.com and DomainB.com are actually the same server/IP, but I want to
send the user through Response.Redirect() to that second domain.

I have no problem reading the current Host, Port, etc. from the Request.Url
object. But my problem is, let's say I want to send the user to a different
place on the site too. For example, I want them to be on a different domain
AND a to go to a path that would normally be done just be writing
Response.Redirect("~/Something/XYZ.aspx")

The problem is, I don't seem to be able to figure out how to properly BUILD
the path AND switch to a different DOMAIN into a single new URL.

Help?

Alex