Thanks so much for the quick responses!
I do, in fact, have a Harmony remote. Currently in my Harmony configuration, my Flirc is using the Panasonic TC-P65VT30 profile. Am I understanding you correctly that I'd need to set up my second Flirc using another profile (not the Panasonic)?
I'm looking to use my Harmony remote to control two separate HTPCs, each with its own Flirc.
Thanks again!