IMO Nintendo would be better off just accepting a deal with Microsoft. They could take control of the XBox division and retain a good chunk of the licensing fees/royalties and keep control of hardware design.
Microsoft would allow it because I don't think Microsoft is really all that enamored by the game business anyway. They like the prestige the XBox brand gives them, but letting Nintendo take management of said brand over I think they'd be OK with that.
Nintendo could also release games for Windows PC in that scenario.
Sony can't match that deal because I doubt they'd be willing to share control and licensing fees of the Playstation division with Nintendo. It's a better deal for Nintendo than just turning into a regular third party.
A joint Nintendo + XBox platform would sell at least 50-60 million consoles (plenty for Nintendo to gain a wider audience), have all the third party support, and they'd also have Windows PC users to tap into, which is tens of millions more in consumers.
