In IIS, it is possible to listen for many DNS names on one IP address and port and then direct users to different websites based on the DNS name.
Is the same thing possible with F5 Big-IP devices?
Yes. This can be done with either HTTP Class profiles or an iRule on the virtual server you are configuring.
A sample iRule to get you started would look something like this:
I suggest using F5's DevCentral site at http://devcentral.f5.com/
This is possible, though it requires writing iRules for them and associating the iRule to the virtual server. I don't believe there is a GUI way to do this.