Is a multi-wire branch circuit with shared neutral acceptable?
As long as the circuits are on different phases there's a decent chance this is safe as is, but it's a bad idea to wire this way in a home and a good idea to fix it.      You can't be sure of what's behind the walls but your solution might completely repair the situation and will be no worse.  Better to attach your new run to an outlet than a light.  If you use a light be aware that some lighting circuits are powered from the ceiling box, others are powered from the switch box.  Make sure to connect to an unswitched point in the circuit.

The style of wiring you found is common in large commercial installations.   It is simpler and cheaper to reduce the number of neutrals running around the place by 1/2 or 2/3.  If using conduit and individual conductors it saves pulling extra neutrals for nothing.   But the key is that it has to be designed and maintained properly.  All the circuits sharing a neutral have to be on different phases.   If an installation is designed so that ALL its circuits are run this way, and if professional electricians do all the maintenance over the years and decades, this will work fine because everyone knows what's going on.  But in a home, those are terrible assumptions.   If one of the breakers on a circuit like this fails, and is replaced, and the new one is on the wrong phase (because the homeowner doesn't know it was done this way or even a pro doesn't realize) then the neutral will be overloaded and the breakers won't protect it.  Also, if a homeowner turns off one circuit to do maintenance he won't realize that there are live wires in the junction box he's servicing or that there could be a dangerous voltage across a broken neutral during servicing.