I don't see a problem with this as long as neutral uses a gauge high enough to support both branches. Am I missing something here?
Here's an illustration:
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To those who know all about MWBCs, this particular case is bizarre, interesting, and falls in the "you learn something new every day" category. Please read carefully and not leap to conclusions. Thank you.
The circuit breakers on the diagram are not feeding opposite phases, but the same one. means this is a shared neutral which is not a MWBC.
And this (a non-MWBC) is an area often messed up by electricians, so it is generally frowned upon quite a lot.
There are old circuits out there like this. This is is "leeeeeegal" per NEC... look at 215.4(A), or 225.7(B). However these apply to feeders, and outdoor lighting, respectively. You must upsize the neutral to handle the current for all the circuits which are on the same phase.
However, as a practical matter, any authority able to do so is going to nix it. Prepare to have your installation fail inspection, and your protestations of being allowed in Code fall on deaf ears.
Any installation like this has some rules.
You must pigtail all the neutrals, except where a pair of wires branches off from the group and doesn't come back. That is because removing a device on one circuit (e.g. a receptacle) mustn't break the neutral path for any other circuit.
You will also need a common maintenance shut-off, powering down all circuits which share the neutral. If your circuits come out of a fuse panel, a shut-off switch will suffice. Common trip is not required; i.e. all the circuits don't need to shut off together if one overloads and blows a fuse or breaker. However with breakers, those are the shut-off, so they must be handle-tied to shut off together. Rather than chase around looking for handle-ties, most people just use a 2-pole or 3-pole breaker. They will have the side-effect of common trip; again that's not required.
Increasingly, GFCI or AFCI protection is being required - most rooms in a house must be one or the other. GFCIs are simply not built for shared-neutral circuits.
It is possible to use a GFCI or AFCI on a multi-wire branch circuit, which is a special case of a shared-neutral circuit, in which each circuit is intentionally on a different phase. In this case the neutral carries only differential current, and can be the same size as the other conductors.
Generally a multi-wire branch circuit is the only kind of shared-neutral circuit an authority will allow you to have.