The secret one at Junidy was in TTA, it's not canonical?
You and Wil aren't quite talking about the same thing. Let me explain.
I believe that Wil thought - and he'll please correct me if I'm wrong - that you were asking about the institutes which are
Imperially operated and not about institutes which are
located within the Imperium.
Canonically, we know of two Imperially operated institutes; one in the Marches and one on the Rim. They're the two institutes whose charters were reinstated in 1014 after between revoked between 800 and 826.
Canonically thanks to
TTA, we also know about an secret underground institute on Junidy. While it's an institute in the Imperium, it's also an institute operating illegally and in defiance of Imperial laws.
Getting back to your question - which I believe is regarding illegal underground institutes -
IMHO while institutes know of each other, they deliberately don't know any of the details regarding each other. Like any well run underground movement, they're going to practice a cell structure.
The "cell" on Junidy may know that other "cells" exist in other systems. What the "cell" on Junidy doesn't know, however, is how to directly and quickly contact those other "cells". They'll know how to send messages through a series for blind drops and cut outs, but they won't know that you contact the institute on Mora by walking down the alley behind
Clock's Sanitary Luncheonette, tapping "shave and a haircut, two bits" on the 3rd door on the left past the grease tank, and whispering
"Swordfish".