I'm reading Japanese Harry Potter (賢者の石）I am nearly at the end and there is this grammar that I have encountered twice so far that I have no idea how to interpret. The two sentences with this grammar that I have found:
My attempted translation would be:
1: In the middle of town, a man shook hands firmly with Harry and then left without saying a single word. 2: It was that very same day when he met Quirrel at Leaky Cauldron and shook hands with him (wasn't it?).
I find it strange that both times this structure was paired with the word 握手 although I feel like that's probably just a coincidence.
I have no idea what the までして (I'm assuming it's from までする) means here. Using まで as "until" makes no sense to me here and using the meaning "even" which apparently まで can have as well makes little sense to me either. Any help is appreciated, thank you.