This sounds like a good way for them to co-exist. Roxy and Smudge
do something similar.

Roxy and Licky have a funny little etiquette around playing the
"stick-poking-in-and-out-from-under-the-rug" game.

I'll run the stick under the throw rug, letting it poke in and out
along the edge. First Roxy trots off to a distance of about 5 feet
and watches intently, then races toward me and attacks the stick
ferociously, scrunching up the rug (which is on top of wall-to-wall
carpet, so it's not that easy to scrunch up!). She'll do this once
or twice, and then Licky, hearing the exciting sounds from wherever
he is, ambles in and wants to play, too.

The two of them will then sit and watch the stick, and I'll see them
look at one another, and I swear, Roxy is sort of nodding toward Licky
as though to say, "You take this one, I'll get the next." It reminds
me of musicians signaling to each other when to take their solos. :)

Joyce

Sounds a bit like the girls, since we put the basket chair by the fireplace.
It's big enough for two of them, but Cali isn't willing to share. So they
have been taking turns.

LOL!  How lucky you are to have not one, but *two* chest warmers!