Here’s an interesting thing: If you make a search on Basketball Reference with the criteria > 10 PPG, > 6 RPG, > 6 APG, > 2 SPG you will see the most well rounded guards/forwards: Michael Jordan, Magic Johnson, Larry Bird, Lebron James, Russell Westbrook, Jason Kidd, Scottie Pippen, Walt Frazier, Rick Barry, Fat Lever etc these are the players most likely to get a quadruple double with steals.
Getting 10 steals is remarkably difficult though; I think its interesting that Jordan, Magic, Kidd, Lebron etc never got a quadruple double before.
Using the criteria for blocks, you have to set it to > 10 PPG, > 6 RPG, > 4 APG, > 2 BPG and you can see some of the most well rounded big men: David Robinson, Kareem Abdul-Jabbar, Kevin Garnett, Bob Lanier all appear on the list pretty frequently. Wilt Chamberlain would have also been on there. Curiously, none of them except Robinson have produced a quadruple double, and Hakeem doesn’t appear on the list. Kareem had several seasons of statlines like 27/14/5/4 so I’m surprised he never had a quadruple double too.
Modern day, players are averaging triple doubles left and right so I will start with the most likely candidates: Anthony Davis, Draymond Green, Lebron James, Russell Westbrook, Ben Simmons would be my picks. Davis is currently the player most similar to Hakeem and Robinson too.