The OP
We've been assuming that this is a 120/240V single phase system, instead of a 120/208V system. Is this correct?
In a 120/208V system, the line currents would only partially cancel in the neutral even when there are equal loads on the two phases (because they are 120° apart instead of 180°). But it would still be OK to have a MWBC with the common neutral having the same ampacity as the two line conductors. The neutral would count as a current carrying conductor. however.
A few examples:
16A on L1 and 16A on L2 would have 16A in the neutral conductor.
16A on L1 and 8A on L2 would have 0.866 x 16A = 13.85 in the neutral.
16A on L1 and 0A on L2 would, of course, have 16A in the neutral.