This is a really dumb idea. I wouldn't ever do it, because it's ridiculous, but the thought popped into my head, and I just had to ask in case anyone's tried it:
Imagine a scenario:
There is a sprite (diminutive),
who uses a brownie (tiny) as a mount with a custom saddle,
who in turn rides a gnome (small) as a mount with a custom saddle,
who rides a human (medium) as a mount with a custom saddle,
who rides an ogre (large) as a mount with a custom saddle,
who rides taiga giant (huge) as a mount with a custom saddle,
who rides rune giant (gargantuan) as a mount with a custom saddle,
who rides a great wyrm red dragon (colossal) as a mount with a custom saddle.
Imagine all of them (except the dragon) have Mounted Combat.
1. Is this physically allowed?
2. How far down the chain can the Mounted Combat feat be used to avoid hits?
2a. Can the Rune Giant still roll for the Dragon, even with all the other stuff?
2b. Can others in the middle roll for the step below them, even though the dragon is doing the movement? For example, can the human roll to make sure the giant avoids an attack?
2c. Can you roll further down the chain? Could the sprite roll for the dragon?
I would rule against it.
Why? Because the rider is controlling the mount's movement... so the mount (being controlled) couldn't then ride another creature. (at least not such that they could use the skill).