The license that prevents use by a particular list of corporations can likely be easily crafted.
But because any particular invention about LLMs is not a specific product but an approach, it would just be re-implemented.
One could imagine patenting an approach, if it ends up being patentable, and then giving everyone but some excluded entities a grant of royalty-free use. But, unless the use if that particular approach is inevitably very obvious (which is really unlikely with ML models), you would have hard time detecting violations and especially enforcing your patent.
But because any particular invention about LLMs is not a specific product but an approach, it would just be re-implemented.
One could imagine patenting an approach, if it ends up being patentable, and then giving everyone but some excluded entities a grant of royalty-free use. But, unless the use if that particular approach is inevitably very obvious (which is really unlikely with ML models), you would have hard time detecting violations and especially enforcing your patent.