I think your drawing is OK in Massachusetts, see page 95 of the document linked to here, sounds like section (9) stack venting:
https://www.mass.gov/review-248-cmr-1000-uniform-state-plumbing-code
[If this is your first time reading a code, it is best not to assume you know what any of the words mean but to check each one in the definitions section at the front. Only if there is no definition is it safe to assume a word has its normal meaning.]
If I'm reading that page correctly, then (in Massachusetts) you can do what you propose in your last paragraph only if the bathroom is not on the top floor of the building.
Cheers,
Wayne