While playing Fallen London, I keep seeing this Opportunity card turn up (minor spoilers) :
It seems like there are some interesting options here, but as you can see, I'm not yet acquainted with any of these individuals.
These acquaintances are unlocked in several places, and they have storylets for increasing your friendship with them, usually via buying them something or doing a favour.
The Repentant Forger - If you end up with your Suspicion above 8, you'll be thrown in New Newgate again, and can meet him via an Opportunity Card. Befriending him will allow you to meet him in Veilgarden, where he can help you with increasing your Fascinating quality.
The Regretful Soldier - You can met The Regretful Soldier via an opportunity card while in Watchmaker's Hill, as long as your Dangerous quality is above 45. If you talk him down and prevent him from fighting (which involves having a Persuasive quality of around 45), he'll become your friend.
The Sardonic Music-Hall Singer - A character within the 'Missing Person: Absconding Devil' series of storylets in Ladybones Road (unlocked at Watchful 12), as well as the 'Bag A Legend' ambition. She also appears in an Opportunity Card that is unlocked with a Persuasive quality of at least 89. Each of these will let you befriend her.
The Wry Functionary - If you attend the Ambassador's Ball in Veilgarden (Persuasive quality of 56 needed) and get the 'The Darling of the Ambassador's Ball' quality as a result, you'll be able to correspond with him via another storylet in Veilgarden. On a rare success, you'll gain him as an Acquaintance, and you can meet with him in the Shuttered Palace once you gain access to it.