Sophia is invited to the concert when/if Sam has maximum points, no other conditions.
During the concert in relation to Cathy we have two situations (Sophia refuses Aiden's 3rd task or continues) we have a message/call scene from Liam.
The situation where Liam meets Andy/Cathy alone was unrealistic from the start.
If Sophia returns home with Patricia I think Sam's route cools or disappears.
Once home Sophia will change clothes being the same scene for both routes (with or without Aiden).
We can think of two situations: Sophia waits for Liam or she goes alone to Cathy's apartment.
My guess is she will wait for Liam and they will leave together. I say that because this situation gives the possibility of another round between Sophia and Sam. If she leaves alone she would go straight down to the taxi/car, but if she waits for Liam, once dressed she can go out to the backyard waiting for Liam. The situation would limit Sam's hand access to too many of Sophia's assets
. The next teaser, depending on how Sophia is dressed, will tell us how far Sam's hand goes.
I say all this under the assumption that L&P will not break Sam's event in two, before Cathy and after Cathy
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If Sam's part 2 takes place in the backyard it can also be used for the "dylan_cuckold" route, and Liam can create a situation to L&P's liking: coitus interruptus.