Mikado Sanzen'in is Nagi's grandfather and runs the Sanzen'in family empire—supposedly built on oil money, though he's never exactly transparent about it. He lives in a sprawling mansion that makes Nagi's place look modest, complete with an entire staff of identical-looking servants.
The guy's got an almost supernatural ability to read people just by looking at them. That said, despite being Nagi's only living relative, they have a pretty rough relationship. Nagi actively dreads visiting him at the main house, which is why he basically disappears after his first appearance in the story.
Still, it's clear he cares about her, even if they don't show it well. When assassination and kidnapping attempts start circling around Nagi, Mikado tries to shut them down—though his methods are. questionable. He initially threatens to pass the entire Sanzen'in inheritance to whoever can make Nagi cry and beg for his forgiveness, which is honestly a messed-up way to handle family drama. He dumps that responsibility onto Hayate. Eventually, with Maria's influence (who he seems to actually like), he shifts gears and decides the real priority is just getting rid of the butler instead.
Content compiled by AnimeList.moe from publicly available sources.