The question arises not just because Oracle recently announced that two executives are the company’s new CEOs, succeeding Safra Catz, who had been CEO or co-CEO for the past 11 years. Making the succession more intriguing, Catz has been elevated to the board of directors with a previously unheard-of title, while founder Larry Ellison continues as chairman of the board and chief technology officer, but with duties that are by no means transparent. Result: We know who Oracle’s CEOs are by title, but who they are in reality may be less obvious.

The stakes in Oracle’s unique succession experiment are extraordinarily high. The company’s stock has suddenly rocketed, doubling in the past four months, making Oracle the world’s 12^th most valuable company. It’s a magnificent performance, but investors might like to know, especially now—who’s really running the show?

In the plain-vanilla version of managing a big corporation, it’s simple: The CEO runs the show, and the board oversees the CEO and overall management of the company. It doesn’t wade into day-by-day decisions. But at some companies, 11% of the Fortune 500, the board is led by an “executive chair” who is not the CEO but who participates in the company’s management while also running the board. Typically, the executive chair is the previous CEO, and the new CEO typically reports to that person. “When you’re executive chair, the buck stops with you,” says Charles Elson, a corporate governance expert who has served on multiple boards. “It’s a title change with little meaning. You’re still running the show, period.” Think of it this way: “executive chair” = “real CEO.”

At Oracle, the board made longtime CEO Ellison executive chair in 2014, and Catz and Mark Hurd became co-CEOs. But then things get murky. Ellison quickly stopped calling himself executive chair and adopted his current title, though the company doesn’t seem ever to have announced any change in his role. (Oracle declined to comment.) Catz and Hurd continued as CEOs until Hurd took a leave of absence then died in 2019, after which Catz carried on alone.

With that as background, look at Catz’s new title: executive vice chair of the Oracle board of directors. It’s a bit odd because in corporate governance, “there is no such title as vice chair of the board” says Elson. Corporations are required to have boards, and boards must have chairs, but that’s it. In addition, it’s hard to see how a board could include Catz as executive vice chair, even as an honorific title, unless it includes Ellison as executive chair, in reality if not in title; otherwise the vice chair would hold more power than the chair.

All of which suggests that Oracle’s new CEOs, Clay Magouyrk and Mike Sicilia, may not quite be CEOs in the usual sense. With two of them, the corporate bucks never fully stop with either. Plus, with at least one board member who is also a declared executive, they’re outranked.

So how many CEOs does Oracle have? Officially two, arguably four. And who knows, maybe it will all work spectacularly. What we know for sure is that no matter how this setup goes, CEOs, directors, and ambitious executives will study it for years.