tedsander

It depends....
For the old 72mHz systems, no.
Depending on the brand, modern 2.4 systems are a possibility. Many actually allow up to 16 servos (or more!), but how to do it may vary. The receiver may only have a limited set of pins for connecting, but may also have an "SBUS" type connection that can allow more. No real standard between brands, so some research needed to determine if the one you are interested in can do it, and what else is needed.
Some brands do allow for running 2 or 3 receivers at once for the same model, which also achieve your goal. The limit then becomes whatever the transmitter can actually send.
Of course, to do any of the above usually means moving up in price for the more top-of-the-line equipment.