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Four Men and a Food Odyssey

William Ackman arrived at Nelson Peltz’s office in 2007 bearing candy bars, soda and an idea.

The activist investor wanted to know if Mr. Peltz was interested in teaming up to push for changes at Cadbury Schweppes, the iconic U.K. chocolate and soft-drink company.

But Mr. Peltz, a veteran at activist campaigns, was way ahead of him. The Trian Fund Management LP co-founder already had a plan in place to press Cadbury to part with its soda business. The spinoff, which the company announced later that year, paved the way for Kraft Foods Inc.’s $19 billion purchase of the chocolate maker in 2010.

“We just rode his coattails,” Mr. Ackman said last month at CNBC’s Delivering Alpha Conference.

Eight years later, Mr. Ackman is again following in Mr. Peltz’s footsteps. His Pershing Square Capital Management LP earlier this week disclosed a $5.5 billion stake in Mondelez International Inc., where Mr. Peltz serves on the board. Mr. Ackman thinks Kraft Heinz Co. KHC -1.63 % could potentially buy Mondelez, according to people familiar with the matter, a deal that would reunite the sprawling Kraft empire that was broken apart in 2012.

This time, the cast of characters is larger. Kraft Heinz is controlled by legendary investor Warren Buffett and his Berkshire Hathaway Inc., BRK.A -0.09 % as well as 3G Capital Partners LP, the investing firm co-founded by Brazil’s richest man, Jorge Paulo Lemann.

The clustering reflects evolving personal relationships among the four men. Mr. Ackman is an acolyte of Mr. Buffett, and he is personally invested in 3G...