Were the building envelopes exceeded by the neighbors to the same extent as by you? If the neighbors only exceeded them slightly, for example, this may still be at the discretion of the building authority.
Is the relationship so broken that you expect to receive no approval?
Well, (not the OP) but that wouldn’t be the first neighbor who isn’t so thrilled when a gap next to them is filled. Usually, everything just gets tighter and maybe there’s also some shadowing somewhere where there wasn’t one before, etc. Generally, people also simply become hesitant when they are supposed to confirm something disadvantageous to them in writing, even if they are otherwise nice people. Then suddenly a basic "no, I just don’t want to sign this" can come up. In that sense, I can initially understand the question "can't this also be done without," even if the neighborhood relationships should be decent so far.
As a rule, the consent of the neighbors whose interests could be affected from the perspective of the building authority is required. For example, if the building envelope is exceeded to the east, the neighbor to the west does not necessarily have to agree. Without details about the situation, one cannot really say anything about it, but if the building authority has already made this requirement, it will hardly back down from it...