"overo" just means anything except Tobiano, so yes, of course, even Arabs have Sabino and Splash- do Falabellas have Frame? Pretty sure they do but would like a definite answer on that one....
The only pattern that really carries the name "overo" these days is Frame, the other two patterns, Splash and Sabino are seperate and definitely in Falabellas. We are not sure of Frame, however....
I can answer that Jane , yes Falabellas do have Frame, I used to own one , Diane Im sure you have him in your data base , Micatos milltown Magic , he is visually solid black with two blue eyes , he tested positive LWO
if you want to study the bloodlines to see where it came from Ive attached the pedigree info on both of his parents although it does seem to have come from his dam toyland side
he produced splash and frame babies ,it looks like the splash also came from mum although his sire did have socks so who knows , heres a pic of Toyland Patia , not great but its all I have ,
the only purebred that I can tell you had frame was "Celticmist Firecracker" but he died of colic six months after I sold him I cant say for sure if he also had splash but he did have a blue eye , most of Micatos Milltown Magics foals were blends and none of them had loud frame markings ,several had blue eyes in fact most of them had just a star and a snip sometimes with a tiny white coronet so Im pretty sure that he had some kind of restriction gene ,