Companies already license out their source code to whoever they wish, and many already do what you suggest ("enterprise licensing"). Many prefer to open-source non-critical software, because the community can help maintain it.
Enterprise deals that include source usually do not allow the recipient to publish modifications to the code and come with a variety of other very serious restrictions. I am talking about something quite different.
Also, I disagree with your stance that the GPL "entirely upends" the possibility of making money off licensing software. Trolltech were (until they were bought by Nokia) an example to the contrary; Qt was dual-licensed under the QPL and GPL for years and they were obviously making money out of all the companies that didn't want to have to GPL their product.
Finally, it's not really clear to me that anyone really wants this model; there are companies (like iD) who are keen to open source at least some of their software. Many other companies are not interested in releasing any at all. It's not at all obvious to me that there is some sort of middle ground of companies who want to release their changes but only to other companies who have licensed the same software, thus forgoing the whole feel-good factor of open source, arguably much of the point of it and certainly the entire Free Software angle.