Is this sound change plausible?

Greetings,

I was doodling out a new language sketch, which contains an open /O/ and
close /o/. Later, as I went along, I kept finding myself wanting to
change /o/ to /2/ (i.e. as a development from a parent language to a
daughter language). Now I know that in several languages (such as
English and Occitan) original /o/ changed to /u/, but is /o/ to /2/
feasible? I can't think of any natlang I've encountered it in, so I was
wondering if anyone else has, or if someone more knowledgeable in
phonetics and/or historical linguistics could tell me whether it is
possible/plausible, or if it would never (or not likely) happen in a
"real" language.

Thanks,

Thomas

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