The only downside to Joe's suggestions are redirects. For example, let's say that the user types in blah.domain.com/support and the Host header is changed so the web server sees www.domain.com/support. Let's assume support is a directory. The web server will now redirect the browser to http://www.domain.com/support/. So you also need to modify the URI in the redirects so that the client sees http://blah.domain.com/support/.
I believe everything you need to do can be quickly accomplished with my ProxyPass iRule (http://devcentral.f5.com/wiki/default.aspx/iRules/ProxyPass.html). The rule itself is fairly complex but you should not need to modify it. Instead just create the data group as described in the instructions and the rule will take care of the rest. If the rule doesn't do what you want let me know and I'll review your configuration, etc.
Nimbostratus