An Infrared remote just outputs a sequence of signals, a multi remote
could learn those signals if it knew the code, if they were in its
memory, thinking more about it, they probably are not in the memory of
the program of the multi unit but could learn it from a second original
remote.

R.F. Transmitters for lighting, apliance from Leutron, X 10, Smart
Home , Radioshack, Smart House and others using that protical are
compatible with GM , Ford , Genie, Kenmore, etc, etc etc. In other words
your Caddy or GM or Ford with 3 button built in door opener can control
X 10, Radioshack, Leutron and other lights from the 3 button handheld or
built in 3 button door openers in your car. I turn on inside house
lights from a Caddy , programing was easy. But the car, garage door
opener, lighting manufacturers won`t tell you this, they want you to buy
their higher priced system by having you think theirs is exclusive. 3
button remotes have 2 extra buttons, you could have your car turn on a
coffee maker and electric blanket if you wished.