Secondly, has this just started, or has this always been the situation
with your little brood?
In physics, it's relatively easy to calculate the movements of two
objects in space (taking into account gravity and momentum), but when
you add a third object it becomes exponentially more difficult.
This is the way it works with cats. Every time there's a change in the
local cat population, they need to do their cat-dance to figure out
the pecking order.
Another question is whether Billie is ill.. the other cats may be able
to notice this where you can't. You may take her in for a quick
checkup (this is just my guess, unsupported by cat experts, but an ill
brood member is often singled out in wild populations)
Also, how many litter boxes do you have for all these folks? If it's
litterbox aggression this may very well be due to too few in the
Finally, in my experience (and I'll be corrected if wrong, no doubt)
females in general are at the top of the social order. Even a spayed
female will usually pull rank in a house of neutered males (which has
been my own experience). However, there may be a struggle with
spayed/non-spayed females. I don't know if there's any accepted wisdom
on how these things work themselves out.
Good luck! Let us know how things proceed.
10. I am your cat.