The world's richest person, Elon Musk, has revealed via tax filing that he now owns a 9.2% stake in the social media platform Twitter Inc (TWTR  ). The $3 billion stock purchase represents a tiny fraction of Musk's $300 billion net worth, and analysts say a complete buy-out is a serious possibility.

Musk himself is a prolific Twitter personality with more than 80 million followers and a history of controversial activity.

In the past, Musk, Tesla's (TSLA  ) CEO, has faced significant regulatory penalties for posting about the company's plans. Those penalties include that any of his tweets relating to the business must first be approved by a Tesla lawyer, but Musk is trying to get that judgment overturned.

However, Musk is also an outspoken critic of the platform: he recently held a Twitter poll to ask whether or not users believe Twitter supports free speech. 70% of respondents answered "no".

The tech billionaire also recently tweeted that he was considering building his own new social media site. With a big enough stake in Twitter, he may not have to. While Musk's regulatory filing suggests that he intends to be a silent Twitter shareholder, most don't expect that silene to last long.

"It does send a message to Twitter ... having a meaningful stake in the company will keep them on their toes, because that passive stake could very quickly become an active stake," said the managing member at Great Hill Capital LLC Thomas Hayes.

Twitter may also be in a particularly vulnerable place. Long-time CEO and Twitter founder Jack Dorsey stepped down from his position and was replaced by the current CEO, Parag Agrawal, in November of last year. Unlike Amazon (AMZN  ), Google (GOOGL  ), and Facebook's (FB  ) founders, Dorsey doesn't get special voting rights over the company's future.

On top of the transition of power, Twitter also announced lofty goals for its 2022 and 2023 revenue and user growth, putting even more pressure on Agrawal.

Since April 1 last year, Twitter's share price has fallen 38%. After Musk's stake was revealed, share prices shot up 25%.

Musk is now the largest Twitter shareholder with 73.5 million shares. Twitter's second-largest shareholder is Vanguard with its 8.79% stake. In comparison, Dorsey owns just over 2% of the company.

"Musk's actual investment is a very small percentage of his wealth and an all-out buyout should not be ruled out," analyst Angelo Zino with CFRA Research wrote in a client note.