Marvelous!
Healthy gorgeous looking plant!
Give it a good soak and remove the current pot...you may have to cut or break it off.
Then remove as much media as you can while minimizing root damage.
It appears it is likely related to the genus oncidium.
Use a medium sized potting mix for oncidium types...NOT course like that for catts and phals.
I would split her almost down the middle if I could
When you are de-potting her and freeing up the roots, you will most likely note a weak point where she can be separated.
Frequently, when I have the same situation, I find back bulbs in poor condition and instead of splitting, just have to break them off; so pay attention as you go
These plants prefer to be tight in the pot! So remember that when choosing your pot size.
I like clear plastic as well so I can see my roots at least a bit.
Congrats on your lovely plant(s)