Identical websites accessed with different URL's

If I may add, what you're attempting to do is not easy. It's straight forward enough to replace headers and URIs on the way in, but another thing entirely to replace the headers and URIs in the payload on the way out. There are some tools like the ProxyPass iRule and the rewrite profile in 11.4 and above that will do this mapping for you, and it may even be worth your while to create the 4 applications on four internal VIPs with separate ProxyPass or rewrite configs, and then use an external layered VIP to pass traffic to the internal VIPs according to URI pattern. You may also want to consider just putting the 4 applications on separate VIPs with separate IPs and use Hosts entries or DNS to move between them.