In all honesty Sony should back off and let Nintendo have this. It's not going to do them even any good if Nintendo goes out of the hardware business and it's a tough enough concept to sell trying to tell kids not to use their iOS/Android tablet as their go to entertainment device on the go. Nintendo benefits Sony to an extent by getting a lot of kids hooked on physical gaming (button gaming). If they go, you're going to have a ton of kids playing nothing but $1 touchscreen games for much of their childhood and it's going to become increasingly difficult to get them onto $400 consoles.
If I'm Nintendo and this doesn't work out and part of the reason is because Sony decided to under cut, I'd strongly look at backing the XBox in response.
Focus on the Playstation 4/5 and VR (which has a ton of potential) Sony.