When several schools sit the same paper, a pupil's result stops being a number inside one building and becomes something comparable. That comparison is only worth having if it is clean.
Blind by construction
A marker should know a script by a code, never by a name or by a candidate number that could be traced to one school's register. The strongest way to keep marking blind is to make sure the marker's screen never receives the identity in the first place.
Everyone writes, everyone reviews
Each school contributes teachers who actually teach the subject. Questions are written by the people who teach it, reviewed by others, and sealed before the sitting so the paper cannot change underneath candidates.
Two releases, two decisions
The host releases results to the schools. Each school then decides when to release them to its own students. That order protects a school from learning that its children's results were published somewhere it had not yet seen them.