I'm surprised there wasn't a ticket for this. Maybe I just couldn't find it.

In short, I want to do something like:

class Monad m => MyMonad m where
    type AssociatedMonad m :: Type -> Type
    default type AssociatedMonad m :: (m ~ t m', MonadTrans t, MyMonad m') => Type -> Type
    type AssociatedMonad (t m') = t (AssociatedMonad m')

    fun :: Foo -> m ()
    default fun :: (m ~ t m', MonadTrans t, MyMonad m') => Foo -> m ()
    fun = lift . fun

The syntax is a bit weird, but I hope in the process of implementing constrained type families the syntax properly analogous to the term-level would shake itself out.

The use-case, like the normal method original, is to assist with monad transformer boilerplate. MonadTrans wouldn't be enough, but MFunctor from mmorph might be depending on the method using the associated type.