So let's look at Liberty:
Women's had Denmark, USA, and Canada. Also Joelle Forte who either is or isn't competing for Azerbaijan. At times, you'll see a Mexican competitor or a Taipei competitor.
Men's: Canada, USA, ITA. Sometimes you'll see Puerto Rico (back when Rohene Ward competed for PR). Viktor Pfeiffer (AUT) sometimes competes.
Pairs: US & CAN. That's usually it. At Indy pairs, you might get Takahashi/Tran (JPN) as well.
Dance: No dance competition at all.
LPIDC dance draws from more than 4 federations, but has no other segments.
Indy Pairs Challenge has pairs only.
So it's doable, but at least 2 competitions would have to merge. Or one of the smaller competitions that has all 4 disciplines would have to enlarge.