Without specifics it's hard to say for sure, but in general unless it's a very expensive horse (like many of the grand prix level horses) I would say not a good idea. One of the key draws of buying my own horse (versus continuing to lease) was that I could make all the care decisions: what to feed, whether or not to shoe, etc. Even if the co-owners are aligned on EVERYTHING (or one of them allows the other to make all the decisions and just wants to ride) what happens if one of them loses a job, gets a divorce, etc?
“The horse is a mirror to your soul. Sometimes you might not like what you see. Sometimes you will.” - Buck Brannaman
"Nothing forced can ever be beautiful." - Xenophon