Activist investors — money managers who seek to shake up a company’s strategy in search of huge paydays — have been growing in size and power in the United States, bending the knees of even the biggest corporate titans.

Now, these investors are taking their fights overseas with bigger and bolder bets.

The latest to step onto the global stage is Daniel S. Loeb, who in his first major European campaign is looking to rattle the Swiss food giant Nestlé.

By taking a $3.5 billion stake, including options — his biggest wager to date — Mr. Loeb’s $17.5 billion hedge fund Third Point is betting that Nestlé can rev up its growth if it listens to Third Point’s proposals, which include selling off Nestlé’s stake in L’Oréal. Investors appeared to applaud Mr. Loeb’s gambit, sending shares of Nestlé up 4.3 percent in trading in Zurich on Monday.

Other European giants have entered activists’ cross hairs. This year, Elliott Management, the $33 billion firm run by Paul E. Singer, took on both the Dutch paint maker Akzo Nobel and BHP Billiton, a British-Australian mining firm.