I somehow assume it’s about semi-detached houses or similar, hence probably the restrictions regarding a uniform appearance.
Back to the core of the matter: maybe a misunderstanding has arisen somewhere? Your drawing with double frames (i.e. 2 x double lift-and-slide door elements) is indeed structurally questionable, as the stiffening frame must be anchored all around in the masonry. Maybe the builder took the proposal literally and is therefore refusing?
However, you do not need a double frame - lift-and-slide door element divided into four parts, just normal, with the frame only around the outside, opening according to scheme K. This is not used very often, as the actual advantages of the lift-and-slide door are somewhat lost, but basically it is possible without problems.
Alternatively: what about three parts, but not symmetrical? That is, fixed glazing in the middle over the width of 2 elements, and sliding doors on the left and right respectively? Maybe this would still be visually acceptable?