New Main Quest: Find Emily in the dormitory
Note - before you set out to rescue Emily, make sure that you have the Golden Cat master key on you that can be taken away or stolen from Madam, who is currently occupying her office on the first floor (the above screenshot).To learn more about how to find Madam and determine Emily's whereabouts, refer to Explore the Golden Cat Club..
Take the staff exclusive staircase and after you pass the first floor, head towards the upper ones. On your way, it is worthwhile to look into one of the side rooms (requires Madam's key) to find gold (you need to look into the chest!), Piero's spiritual remedy and a bone charm hanging on a wall.
Continue towards the upper floors to reach the attic. In the first room of the attic there is a courtesan. Don't let her see you and search the room for gold, food, a book and a rune. In the third room there is gold and food. To end up, enter the second room, in which there isEmily. Listen to the conversation to learn that the girl will wait for you at the VIP door.
New Main Quest: Meet Emily near the Golden Cat VIP door
Backtrack to the staircase and return to the lowest level of the basement, choose the door marked as VIP Exit (the above screenshot). On your way, look around for two Sokolov's health elixirs and a note (Elixir Delivery), and approach Emily to talk to her again. Emily will resolve that she can reach the boat on her own and that she will be waiting there for you. Thus, you won't have to escort her on your own. Note - if Emily doesn't want to leave the location, make sure that you unlocked the door with the Master key from Madam.
I suggest that you turn your attention to the side quest connected with the exploration of the art dealer's flat (subsection Explore the art dealre's flat). I recommend that only after that you consider how to solve the main aim of the quest concerned with the elimination of the Pendelton Twins (subsection Choose your way of eliminating the Pendelton twins).