In fact, the patent system comes close. If what you contributed was inventive and new, you get a patent on that slice of what you invented. For someone to commercialize the whole thing, they may need to pay both parties (essentially both parties who had a part to play in the "discovery" will be paid for their work). In many cases like this, the parties have to cross-license each other (pay each other or license each other for their respective patents).

That is actually what the article says.

"An appeals board of the patent office ruled that the gene-editing inventions claimed by the two institutions were separate and do not overlap."

"Ultimately, companies wanting to apply Crispr for use in medicine, agriculture or other fields might need licenses from both the Broad Institute and the University of California, a lawyer for the university said. ..."