LONDON — JAB Holding Company, the deal-hungry conglomerate, has bought dozens of coffee brands and begun branching out to doughnuts. Now, it has set its sights on sandwiches.

The company said on Tuesday that it would buy a controlling stake of Pret A Manger, the British sandwich chain that is a mainstay of London office workers, from an investment firm to expand its food-and-beverage empire.

The deal was valued at about 1.5 billion pounds, or nearly $2 billion, including the assumption of debt, according to two people briefed on the transaction, who were not authorized to speak publicly.

With the deal, JAB has taken another step in becoming a force in the food world. Since 2012, the company — backed by Germany’s wealthy and secretive Reimann family — has spent tens of billions of dollars to assemble a huge portfolio of eating and drinking brands. (The conglomerate also owns the cosmetics maker Coty, as well as stakes in the household goods giant Reckitt Benckiser and the fashion label Bally.)