Local Connect w/ Multiple connects

Is it possible to connect to the same Local Connection more than once?

What if I have a Flash signature with same flash movie on the page 3 times and I click on the button on the first movie. Can the other 2 movies do the same action the first movie is doing?

I thought thats what LocalConnection was for but when the second movie tries to LocalConnection.connect it says the connection is already connected.

Thanks!