Fixed point of n-mutually recursive functors

I am able to define the fixed point of a functor as

data Fix f = In (f (Fix f))

where I can also define the type class

class Functor1 f where map1 :: (a -> b) -> f a -> f b

I can also define the fixed-point of 2 mutually recursive bifunctors as:

data Fix21 f g = In21 (f (Fix21 f g) (Fix22 f g)) data Fix22 f g = In22 (g (Fix21 f g) (Fix22 f g))

where bifunctors can be captured in the type class

class Functor2 f where map2 :: (a1 -> b1) -> (a2 -> b2) -> f a1 a2 -> f b1 b2

Now, I would like to generalize those definitions to n-functors. Is it possible? If it isn't, what kind of type system would I need? Is it possible using dependent types? I would also appreciate any points to literature using n-mutually recursive functors. Best regards, Gonzalo Flores