I think the relevant language is this:
Parry: "When the character suffers a hit from a Brawl, Melee, or Lightsaber combat check ..."
Improved Parry does not involve a combat check, it merely hits the target with a weapon, so by a strict reading of the rules, the riposte from Improved Parry does not allow for Parrying back.
That said, from a narrative standpoint, it is entirely logical that a riposte can itself be parried (this happens all the time in fencing), so I could see allowing it based on that logic. I don't see any gamebreaking interactions cropping up if you allowed it.