I was thinking that a Switch Pro could be implemented relatively easily. A "supercharged" Switch able to run in handheld mode at the current dock performance levels, and offer even further capabilities (eg 1080/60) in docked mode. Or they could launch a family of products, including a Switch Elite console-only system running certain current Switch games at 4K. How do you think Nintendo could approach this?

They would simply leverage already established technology.
I.E. Pascal based Tegra instead of Maxwell. (like they should have from the start, but that is another discussion entirely.)

If Nintendo retains the use of Tegra however... Don't ever expect 4k.

Either by a newer, more powerful chip or by implementing a supplemental GPU in a dock upgrade. The latter has already been patented so my mony would be on that.

It is just a matter of if they want to do it or not. Nvidia has a chip already that offers exactly what you discribed from a Supercharger Switch, in the Tegra X2. It would be quite easy for them to make a larger SOC for a bigger home only box, adding more CUDA cores, and increasing clock speeds, and using HBM or GDDR. Everything they need is available, it is just a matter of funding it, and putting it to the market.

Honestly this is the point every company is at. AMD, Intel, and Nvidia all have the tech to make a range of products, that spans Mobile, to High End Home Equipment. It is just a matter of companies deciding to put their money into it, and then consumers getting on board. At this point Sony, Microsoft, Nintendo, Apple, Amazon, Google, Samsung, and a few others could easily offer a range of Portables, Mobiles, Tablets, Laptops, Consoles, and PC's, that are all part of a unified ecosystem. It is just a matter of who does it best at this point. Within the next decade, you will be able to play your games on the ecosystem of your choice, via the device of your choice within said ecosystem. Purchase once, play anywhere.

As a gamer, I hope that either Sony, Microsoft, or Nintendo do it right first, and get a large share of the market. So I hope Nintendo does expand and succeed. The last thing I want is Google, Apple, or Samsung taking the rest of the gaming marketshare away from SNM, and seeing them destroy the gaming space like they have done with the mobile space.

Oi, I hope that this doesn't end up happening, it's never going to be able to compete in power wars with Xbox or PlayStation. Unless there are exclusive games for it not possible on the original Switch, like how there are New 3DS exclusive games, I wouldn't think that they would be able to really make proper use of the extra power.

I'd rather they focus on next generation hardware, New 3DS and PS4 Pro just seem so utterly pointless

Trying to get more third party support would be the only incentive for this. Nintendo's IPs really don't need to be on more powerful hardware. Their art styles can be realized as well as they need to be on the current Switch.

They didn't use Pascal? I thought that's why it was as strong as it is?

Man, I'm not sure if that makes the Switch more or less impressive.

It is using Maxwell, Pascals predecessor.
To be fair, Maxwell is pretty efficient, certainly more so than most of AMD's current efforts.

They'd be better off, promptly launching the Switch's successor March 03rd of 2022. Same concept, better hardware, and backwards compatible with Switch. But Nintendo won't do that. They have a bad habit of dropping nearly all support for their current console, waiting a year, and then launching a successor. Wii was nearly unsupported for all of 2012, before they launched the Wii U. The Wii U barely got anything from summer 2016 to spring 2017, when the Switch launched.