"Do tell."

"I think the most promising way to gain the favor of the Duke Metcalfe requires that he distrust the assessment the Lord Metcalfe might provide of you, which seems doable given that he had to bail Lord Metcalfe out of some trouble not too recently, according to one of his friend's sisters. And so it might be wise for you to dance with Miss Henrick, Duke Metcalfe's favorite niece, as well as Miss Anderson, Lord Metcalfe's former ...interest, whom the Duke Metcalfe did not approve of for reasons I won't bore you with, in hopes that this will taint the seriousness with which the Duke will take any aspersions cast on you by his son. Also, if you'd dance with Miss Haster, it would help me by way of a complicated chain of relationships and reactions that involves a besotted habberdasher... I regret not having my notes brought, though I suppose I couldn't be seen going through them anyways." 

Lucette gestures discreetly towards each young lady as she names them.

"The tall one in the pink, the blonde with the ribbons, and the one in the lacy blue dress?" he checks.

"All correct."

Then he will wend his way to these targets and seek to sign their cards.

Based on how other men are doing this it requires flirting with each woman first.

Oh god. Fine. "Good evening, Miss Henrick, how does this ball find you?"

"Excited, though I dare say a bit nervous as well. And you Mr. Swan?"

"I'd imagine your nervousness misplaced, I'm sure you're an accomplished dancer. I myself am little acquainted with this sort of ball but hope to acquit myself on the floor tolerably well; I've been catching up on English dances."

"Oh, have you had the chance to learn the minuet?" Miss Henrick gestures as she asks her question, drawing attention to the dance card tied to her wrist.

"I believe I can perform a minuet, if you'll give me the opportunity to demonstrate?"

"I'd be delighted." She holds out her hand with the dance card for him to sign.

He'll find a slot that is, ideally, a minuet, and not #5, and sign. "I shall look forward to it," he says, bowing over her hand.

And next.

Miss Anderson is no more difficult to persuade into a dance, though its more obvious with her that she's doing it because she considers Haru fashionably exotic. Miss Haster is surrounded by a bit of a crowd when he first approaches.

Can he get a peek at her card to see if he's wasting his time?

Still two slots left!

Hopefully one coincides with his remaining dance slots - ah, yes, he can snag the #8, unless of course he can't. He inclines his head to her rather than immediately try to interject in whatever the cluster of people around her is saying - presumably they're not just standing there silently -

They are having a conversation about how much they admire the renovations to her city manor, though it seems like only half of them have actually seen said renovations.

Lot of people getting renovations. Or maybe it's the same family. "Was it greatly disruptive to the household when they were underway?" he asks.

"Oh no, not at all, we had them done when we were in the countryside."

"And they were all done in a timely manner? I've heard it's rare for a renovation to be as quick as promised, but perhaps they're better at guessing here."

"Oh heavens no, it was supposed to be done in time for a visit during the winter."

"So disruptive after all. I hope your winter was delightful regardless."

"It was, we wintered at my uncle's estate, which had ample room."

"Might I prevail upon you to tell me more about it over a dance? We both have the eighth available, it would seem."