Yes it is the norm.
Many girls are on many agencies. I believe a few agencies are the same outfit operating under different names, but many girls work with agencies who are not connected.
As said here, there are quite a few girls about who are available who can be hire through an agency - or independently from their own means.
Have a good read about from any of the entertainers. Once you have been on here a while you will also be able to get a clear feel from the good to the bad agencies.