HR54R1/700 PAIRING MULTIPLE RC71/73 REMOTES TO ONE RECEIVER. limited to pairing RF wise to only four remotes?

We have one DTV receiver for the living room and kitchen TVs. I have a black box to spoof 5.1 sound and split HDMI to the two monitors. We each have a lose remote at the couch plus I have a third one mounted to the side of a table next to the couch I use to fast forward while my girlfriend and I are holding hands. There is a fourth remote we use at the PC workstation table and a fifth mounted on the fridge below the kitchen monitor.  Every time I program the fifth remote for RF mode it disables RF mode on one of the four other remotes. Is the receiver limited to pairing RF wise with just four remotes?