Armed with subpoenas compelling electronic records and sworn testimony, Mueller’s team showed up unannounced at the home of the business associate, who was a party to multiple transactions connected to Trump’s effort to expand his brand abroad, according to persons familiar with the proceedings.

Investigators were particularly interested in interactions involving Michael D. Cohen, Trump’s longtime personal attorney and a former Trump Organization employee. Among other things, Cohen was involved in business deals secured or sought by the Trump Organization in Georgia, Kazakhstan and Russia.

The move to question business associates of the president adds a significant new element to the Mueller investigation, which began by probing whether the Trump campaign and Russia colluded in an effort to get Trump elected but has branched far beyond that.