Update: there are actually two versions of the Alpine alarm unit. The part numbers are different, but the physically the units appear to be identical.
The early version requires a ROM chip in the alarm unit, and then matching ROMs in the remotes (the remotes work with both versions of the alarm unit). It allows for up to 3 remotes at a time.
The later version allows the ROMs to be "programmed" into the main unit, and then removed and placed into the socket of the remote. it allows non-matching ROMs to be used (i.e. a differently coded ROM in each remote), but I don't know what the limit is. I currently am using two remotes, each with a different ROM inside, so even if two ROMs was the limit, it would still allow for up to a total of 8 remotes.
I have not tried ordering the Alpine ROM kit from the place I linked to above, but having now seen an example of the original packaging, I'm fairly certain that it is indeed the correct part. Land Rover doesn't supply the kit in its own "branded" packaging - instead it just comes in the original Alpine box, and they just slap a little label on it that has the LR part number. Judging from the literature inside the package (and other Alpine alarm equipment from the early 90s), the ROM kit was common to the entire line of Alpine alarms.