Not a snowballs chance in hell.

You're right. I am in my early 30's with a family of five and I buy a crap ton of Nintendo products for the family. 

And by family I mean me and the kids are allowed to play it only when I bring the switch home...

Sony is way more expensive than Nintendo and comes with a huge debt. I'm not sure that is wise. xD

MS could only buy the PS division from Sony though. Microsoft doesn't need any other division from Sony.

I feel like Nintendo buying Microsoft's Xbox division is more likely than that lol.

I don't think that is doable unless Sony was willing to sell. And why would they sell their biggest grossing division? 

So, the only options, pretty much like with Nintendo is a hostile takeover of the whole thing.

But instead of buying each other... Maybe Microsoft and Nintendo could work together? That would be good for the companies and for us consumers.

This! Reapeatedly! Very Loudly!

Let's flip the question around:

Why would Microsoft, a PC gaming and software company, want to buy Nintendo, a console gaming company? The scenario people probably like to imagine is Xbox domination of the console space, but actually, I think Microsoft is A-OK with leaving the console space and focusing on PC, and it would work well for them.

Buying Nintendo would probably go very badly. Maybe if Microsoft bought Nintendo and left them alone except to port all of the big MS games to the consoles (Minecaft, Forza, Halo, etc.) but acquisitions like Nokia and Rare suggest that scenario is highly unlikely. Even leaving Nintendo relatively alone...I think the culture clash between Microsoft and Nintendo would be incredible.