How to configure a pull request quorum making an organizational constraint?
Although I like the idea, based on what I know while working with Gitlab, Bitbucket and Github I do not believe that it is currently possible as I cannot remember that such integrations were available.

Also Googling: github bitbucket pull request approvals integrated did not return any positive results.

I think that the users should always be part of the same organization in order to approve Pull Requests. However, when I think about github I can remember that I was able to invite people as a collaborator even when they were not part or part of any organization.

In conclusion, I think that it is possible, but only in a certain git-server providers like GitHub. My suggestion is to try it and otherwise report an issue in the associate Github project.