No. And Nintendo doesn't need to. People need to stop overreacting everyone should buy everything. Why would the hottest selling platform need to be reactionary to desperate moves of the worst-selling platform maker?

I can see them purchasing a smaller developer like PlatinumGames, but the internet's been saying larger companies like Capcom or Sega, but I can't see a reason they would do that.

Legally... or practically?

Legally, probably not. At least going by US corporate law, investors (by which I assume you mean stockholders) cannot in any way force a corporation to tape any particular action, unless Nintendo has some weird corporate rules. 

Stockholders typically don't have any direct power over the board of directors. If the board of directors and stockholders disagree on a course of action, the board makes the decision.

That being said, the board of directors is elected by the stockholders and can be voted out. So, the stockholders can try to push the company in a particular direction and vote for board members that will do what they want. Whether they would be successful depends on how much stock Nintendo's current officers hold, among other factors.

PG is not looking to be bought and they have well over 200 staff and currently have projects in development not for Switch. Nintendo would not neeed to buy them. They could invest in them. Once Sony had a 20% share in Square. Nintendo could do that. PG likes being independent. They don't need to be owned. Nintendo can do what they always have done as well. Just work closely with a studio. They don't own IS. They are just closely affiliated. Inseperable to the point they don't need to own them. Next Level Games and Hal labs are the same.

Because it shows complacency and laziness which leads to shrinking long term sales, which is a big no-no for investors.

Microsoft is doing all they can to give themselves every advantage to compete and make more money from the Xbox and Gaming division long term. Nintendo's investors see that and will go "Well, what are you guys doing?" 

And not too long ago, Nintendo was the worst-selling platform maker with the Wii U. And people saw their moves of jumping into mobile as desperate and unifying their hardware divisions with a system that was around the same power as the Wii U - foolish. Meanwhile, Sony - the hottest selling platform maker at the time, just kept trucking on business as usual. Now look where Nintendo is now, and look where Sony is now. Granted, Sony's still in a good position, but many are predicting that the PS5 will sell less, and as such, make less, than the PS4, and Microsoft's latest purchase just reinforces that idea. Nintendo and Microsoft have been doing everything they can to catch up while Sony was just kicking back and drinking margaritas, blissfully ignoring the two competitors trying to close the distance. Now Nintendo’s on top and Microsoft is closing the distance. Sony’s investors won’t be too happy about that.

When you're on top, coasting is the absolute LAST thing investors want you to do. They're like sharks  - You smell blood, you go for the kill. Put your foot in their necks.

And they jumped to number one without buying a studio. They just had to release better hardware and games. Nintendo is anything but complacent. We just saw them show 2 exclusive Monster Hunter games that we know Capcom didn't do on their own. They are publishing Bayo 3. We got Astral Chain. They published DQXI. Published Daemon X Machina. They are making deals to publish a lot of stuff. Letting 3rd parties make spinoffs of their treasured IPs. Nintendo is also been putting out new IPs and best versions of est ones. MS has been buying up studios since they got in console gaming and they have yet to be the best selling console. So that has not worked out for them yet they keep trying the same thing. MS manages studios poorly in general. Same old song and dance.

Investors can get new board and CEO elected, but more relevant question would be why would they do this?
Why would that be critical to reasons why they hold Nintendo stock? Just buying more devs doesn't really make
them broadly relevant as MS or Sony (w/ Epic holding) are, it just increases demands to justify investment ratio.
I would compare them to Apple and nobody demands Apple do this or that buyout, or do buyouts generally.
If they already make high profits from their niche market, most would be happy in prudently managing that.
Since it's not really competitive as such, it's not really at risk of decline just from other parties' developments.
Buying out more studios doesn't exactly change the fundmental equation, so how is that such a priority that
would motivate investors to force change in Nintendo policy? Only rationale would be if they think Nintendo
is currently undervalued and such a combo would vaslty unlock it's value, but that's not remotely clear IMHO.

If anything, Nintendo shoudl buy RARE IPs from Microsoft and farm them out to their preferred small 3rd party devs that have been making games for them.

Also lets remember, Microsoft has 300 billion or so in assets. Nintendo has 18.7 billion or so. Buying a company like Bethesda would mean spending nearly half the value of their company. That's a rather huge risk to take. They could like... maybe afford Capcom at best.

I'd rather have them hire and make new teams not just buy IPs. They have so many franchises stuck in dirt already no need to pay to get new ones.