Although never a complete takeover, the Yamaha stake in Korg in the late eighties was controlling ie greater than 50% making Korg effectively a subsidiary of Yamaha. Korg a few years later, made enough money to buy out the controlling interest, so clearly they didn’t want it to continue.
It is entirely possible that a small residual Yamaha shareholding in Korg still exists - I don’t know. But it’s irrelevant, owning some shares in a company does not lead to influence or cooperation. Certainly not the kind of cooperation John is suggesting, which would never happen. That takes controlling interest or an alliance agreement, which typically have to be declared by public companies.
Also, for obvious reasons, members of this forum overestimate the importance of arrangers to both these companies. Even during the time when Korg were effectively a subsidiary of Yamaha, it was never driven by arranger technology, but by development and sharing of much more fundamental sound technology, mostly aimed at synths. Synthesizers and associated products sell in vast numbers. To put this in perspective the DX7 alone sold over 200,000 units. At todays value, that is over $1Bn in sales. One Korg synth sold more than 250,000 units, although at much lower cost than the DX7. In fact musical instrument companies were often wary wary of reputations being tainted in that synth market by involvement with auto accompaniment keyboards.
You can read the 3 part history of Korg here which gives a lot of insight into what really drives these companies.
https://www.soundonsound.com/music-business/history-korg-part-2Mike