Here is a good example of what I mean by not liking to split a Cattleya.
My second plant of Blc Goldenzelle 'Lemon Chiffon' is now fully open. ( to the right my second Goldenzelle) The plant was placed years ago into a square Epiweb basket and grows now vertically with lots of roots hanging down. I would hesitate to chop a plant like that into pieces, unless I absolutely have to.
The pink Cattleya labiata x has a similar problem. It outgrew the wooden basket a long time ago and the whole clump basically also grows mounted.
Needless to say, these Orchids stay in the greenhouse, I just rotate them to the front so we can enjoy them easier, at least I try!