I tried this out in PureScript [1]. I also made each type class have only one member and didn't specify any class hierarchy. I like how it works, but I don't know if anyone else does. It allows you to recreate the category theory type classes [2] if you want to:
class (HasMap f) <= Functor f
class (Functor f, HasApply f) <= Apply f
class (Apply f, HasPure f) <= Applicative f
class (Apply m, HasChain m) <= Bind m
class (Applicative m, Bind m) <= Monad m
E.g., "classOf fmap" as a synonym for Functor.