They are sworn enemies, it's not even possible. Neither would accept. They have tried to work together before, there's no more trust.
Sony used to publish their games on the NES & SNES, it was only when Sony released the Playstation that they stoped releasing games on Nintendo systems. The Playstation itself, as I'm sure you know, started out as a joint project between Sony & Nintendo to create a CD add-on like the Sega CD but for the SNES. For what ever reason, probably watching Sega's struggles with the Sega CD, Nintendo decided to scrap the idea & stick with cartradges for the remainder of the generation & the next. Sony however where still interested in creating a CD based game system & decided to go it alone without Nintendo & created the Playstation.
All this was over 20 years ago, both companies have remained mostly civil with each other & had their own ups & downs. I see no reason that they couldn't work together again.