Liftmaster 800 - Two Remotes

I have a Liftmaster 800 opener, and have been using a Chamberlain 1A5478 remote with it. Access is now need by two people, so I need to program another remote - I bought a generic 433 MHz rolling code four-button remote.

If I clear the original remote, I can program either the replacement or the original (by holding down button "A" after pressing "Learn", waiting for the flashing LED and the flash of the opener's light), but I cannot subsequently program a second (either the Chamberlain or the generic one) - holding the remote button does not make the Learn LED flash; in fact nothing at all happens.

Is there a specific process to add a second remote? 

Thanks in advance.

Thanks for this...