I successfully defended my dissertation in November. Through the process, my chair (member A) was a terrific cheerleader. My second committee member (member B) was encouraging in a more specific,academic manner. At times, only because of Member B's feedback, I advanced in the dissertation process. Committee Member B broached the notion about co-authoring my study. Two days later, Member A called to discuss possible authorship opportunities. I have not given a firm answer. Is it possible to write two articles in separate journals with two different authors using the same study(not the same article)? How does one handle this issue?
There is a general prohibition on publishing the same work twice, whether with different co-authors or not.
One option is just to add both of them on same paper. Put yourself as first author. After that, it's other people riding the sled. Most people understand the main contribution is first author.
Potentially there is some way to carve the study into different pieces and do different papers with each person without violating (1). Or maybe give one of them some later co-authorship (say on a review or followup study). I wouldn't go through too many contortions though just for the purpose of doing separate co-authorships. Divide your overall work as you think it makes most sense to the reader and most benefit to you. Then figure out what coauthors are deserved where.
Also consider to use the "acknowledgements section" if a contribution was made but you do not think it rises to coauthorship.
Finally, I would make sure that A knows about what B is asking for. They may be buddies/colluders or rivals or whatever. But he can advise you. I bet he says go with (2).
Some studies are rich and complex enough that it is perfectly reasonable to publish more than one paper, each detailing some particular novel aspect of the study. Not all are like that, of course, but if yours is you can certainly proceed as you suggest. You aren't limited to just two.
For example, if a math paper has many lemmas to reach a specific result, some of the lemmas may, themselves, be worth a publication. This is especially true if the dissertation is longer than most journals would accept.
On the other hand, in my day (changed fields and am retired now), it was perfectly ok for a student to publish his/her own work without any co-authorship by advisors or others. I don't know if that is still true, but it seems a better practice to me. I would never consider being a co-author with one of my doctoral students on their dissertation. The work was theirs, even when I contributed some things.