"Jane was so admired, nothing could be like it. Everybody said how well she looked; and Mr. Bingley thought her quite beautiful, and danced with her twice. Only think of that my dear; he actually danced with her twice! and she was the only creature in the room that he asked a second time.”(Chapter 3)

Mrs. Bennet believes Bingley confers special attention on Jane by asking her to dance two sets so perhaps it is stretching for me to think Darcy would dance twice with Caroline or Louisa. I think there are two ways to look at a second dance with Louisa. The first is that perhaps it would be inappropriate to dance a second set with a married woman when single ladies are without a partner. Second, perhaps a married lady is safe from speculation. I agree Darcy might not want to give either Caroline or onlookers the impression he is giving her particular attention but then again he does seem to imply he would dance with either of them if they were free. However, perhaps Darcy does not care if people get the wrong impression—somehow that idea does not surprise me. The idea that Darcy might not want to give particular attention by dancing two sets with the SS did spark a question however: How do we know when Bingley presses Darcy to join the dance that he has already danced with Bingley’s sisters? To find something of an answer I started looking at what could be made of the timeline of the assembly ball—it is kind of long so I will answer first and explain second. I think when Bingley presses Darcy to join the dance he has already danced with the SS so if he had engaged either it would be a second set. ;D

The gentlemen pronounced him to be a fine figure of a man, the ladies declared he was much handsomer than Mr. Bingley, and he was looked at with great admiration for about half the evening, till his manners gave a disgust which turned the tide of his popularity… (Chapter 3)

Here I do something which might be considered strange and that is rely on Mrs. Bennet for an accurate description but in this case, Bingley’s partners, I feel she is uniquely qualified by disposition to give the truth of the matter and it is an easy way to divide up the evening--see Chapter 3. She describes six sets of dances plus the Boulanger. If we take just after three sets as the mid-way point of the evening then I will say after the third set is when Darcy’s manners gave a disgust which turned the tide of his popularity after being looked at with great admiration for about half the evening.

Mr. Darcy danced only once with Mrs. Hurst and once with Miss Bingley, declined being introduced to any other lady, and spent the rest of the evening in walking about the room, speaking occasionally to one of his own party. His character was decided. (Chapter 3)

Since Darcy was admired during the first half of the evening then he must have been behaving himself as most of the folks expected he would—at that point he has not begun to show his true colors probably because he is busy dancing with his friend’s sisters. IMO Darcy probably did his duty to his friend and danced with the SS the first and second sets but I admit it could be the first and third or the second and third, so long as he is finishes dancing during first half of the evening—by the end of the third set. The second half of the evening is then when he declines being introduced to any other lady and walks about speaking to no one outside his party.

First of all he asked Miss Lucas. I was so vexed to see him stand up with her! but, however, he did not admire her at all: indeed, nobody can, you know; and he seemed quite struck with Jane as she was going down the dance. So he inquired who she was, and got introduced, and asked her for the two next. Then the two third he danced with Miss King, and the two fourth with Maria Lucas, and the two fifth with Jane again, and the two sixth with Lizzy and the Boulanger." (Chapter 3)

So here I refer again to the obligingly intense observations of Bingley’s partners by Mrs. Bennet. When Bingley presses Darcy to join the dance I believe it is during one of the sets he dances with Jane. I think this because he asks Darcy to let his partner introduce him to Lizzy. I suppose it is possible that Charlotte or Maria might do the office but it seems fitting to me that he would ask Jane. Bingley does not offer to do it himself, I believe either because he is barely acquainted with to Lizzy or because he has not been introduced to her yet himself. He tells Darcy: “But there is one of her sisters sitting down just behind you, who is very pretty, and I dare say very agreeable.” Surely if Bingley has spent even a little time with Lizzy he would know she is very agreeable indeed—just my bias showing though.