What happens after repeated incorrect draw claims?

Question

Assume, one player is in severe time trouble and his opponent chooses to play on. He has a strong feeling that they may have reached the same position for the third time but doesn't have the time to carefully check.

I looked up the procedure in the current FIDE laws of chess

9.5.3 If the claim is found to be incorrect, the arbiter shall add two minutes to the opponent’s remaining thinking time. Then the game shall continue. If the claim was based on an intended move, this move must be made in accordance with Articles 3 and 4.

Can he stop the clock and call the arbiter? What would happen, if he was wrong for the 2nd, 3rd, etc. draw claim?

If it happens more than once, the opponent could claim that the first player was only doing it in order to alleviate his time pressure by stopping the clock and waiting for the arbiter.

Is the worst that could happen that the opponent gets 2 minutes for each incorrect draw claim, no matter their count?

Answer 1

Can he stop the clock and call the arbiter?

A player can always do this. However, according to the rules:

6.11.4

If a player stops the chessclock in order to seek the arbiter’s assistance, the arbiter shall determine whether the player had any valid reason for doing so. If the player had no valid reason for stopping the chessclock, the player shall be penalised in accordance with Article 12.9.

Article 12.9 covers the possible penalties ranging from a warning through to expulsion from the event.

What would happen, if he was wrong for the 2nd, 3rd, etc. draw claim?

The arbiter would decide if the player was being frivolous and if so take action under 6.11.4 above.