I know I am late but after reading the rule book now twice, my answer would be: no, no limit. (Reasoning: It's a follow-up to a reaction and there's explicitly no limit on the numbers of reactions you can take, p. 116 under "Reactions" (Core Rule Book).
Of course, the Doom pay could add up quite rapidly.
There's technically no upper limit, but several practical limits exist.
You have one Standard Attack per round.
You can use a Fortune Point to take another (max 3).
You can spend 2 Momentum on Swift Action, taking another Standard Action. The Difficulty increases per additional action, so you may need to spend more Momentum to get extra dice. (If you don't earn more Momentum, you're going to run out fast.)
Similarly, you can spend Momentum to affect a Secondary Target for a successful attack.
You may be able to Retaliate against an opponent as a Reaction, if they provoke it.
You can Riposte (as per the talent) by spending 1 Doom after making a successful Defend Reaction.
So, though there's a range of ways to attack more than once per round, the reality is that it gets expensive, and you're going to either deplete Fortune or Momentum or add to Doom very quickly.
Depends on how many times you're attacked and how many times you successfully parry.
Attacked once and parry? One Riposte.
Attacked five times and parried? One Riposte per parry.
Then the GM smiles at all the Doom and says "keep it up" :)
This is how I ruled it.
Using Riposte can get costly very quickly. One of my players wanted to purchase it with a starting character. I advised against it because it won't be used very often. I mean please purchase it while rubbing my hands together gleefully with an evil grin.