Insulating from the outside while keeping insulation on the inside

[Garald]

I won't repeat the entire insulation saga. You will know from another post that I'm having some issues in a corner under the staircases, most likely due to a thermal bridge.

 

Bigger picture: I've just finished (or "finished") a renovation where I started being advised by a supposed architect. She made some questionable choices and at least one major blooper (I had strong suspicions and asked here (Nov 2022), people saw laughed out loud - bottom line is, that was caught on time, and she resented enormously from now on). In the end she left the project midway with the money she'd been paid. I finished things with the contractor (who fortunately handled 85% of the money involved) and also with some specialists I found along the way (hardwood, extra windows, etc.)

 

Ah, big twist: she turned out not to be an architect, and most likely never was! No wonder she did not want her contact information to figure on images posted here!

 

At any rate, let us keep our mind on the game. The southern street-side wall was insulated from the inside with 145mm of BIOFIB (R=3.8) - no complaints there. (Plus, it's gradually being filled with books - did I already post pictures of the wall-to-wall bookcase?) According to pictures I took with a thermal camera in January, the northern wall (ISOLIN HPV reflecting insulation + 45mm BIOFIB) is somewhat less satisfactory. Perhaps more to the point, the corners on the ground level on that side seemed very cold, and now I have mold in one of them (under the staircase, as I said). The contractor is of the same opinion as I: it was silly not to insulate from the outside (the only other people at the co-op who ever vote already told me they would have favored it, so no problems from that angle; it's a courtyard wall, so I can't imagine town hall will object), but, rather than undo the inside insulation that we have, we should consider supplementing it with 10 to 15cm worth of insulation from the outside (which I will get done with a different builder - I've seen that this contractor's insurance doesn't cover external insulation).

 

Question: what sort of external insulation can I consider adding, given that I'd keep the ISOLIN HPV + BIOFIB? As long as it's permeable to water vapor, I'm good to go, no?

What do you recommend, keeping the budget reasonable - PIR?