As an alumnus of The Haberdashers’ Aske’s School, I say with some certainty, there is no rule that you cannot have two possessives before a noun the first or previous part of a colon. A word or noun is the same with any part of a colony.

Why is the same meeting as yesterday? In this case, the possessives qualify in a chain: Robert Aske was a freeman of the Worshipful Company of Haberdashers, thus “Haberdashers’ Aske”, and the school was named for his bequest, thus Haberdashers’ Aske’s School.

In our today’s meeting both possessives qualify as meetings and this is what is not

OK. Of course, it’s trivial to make a chain of possessives. Bob’s mom’s dog’s puppy is in his belly

but the teeth there have come through.