South Pacific is the only show to win Tony Awards in all 4 acting categories: Mary Martin as Nellie Forbush, Ezio Pinza as Emile de Becque, Myron McCormick as Luther Billis and Juanita Hall as Bloody Mary. But I know some others were nominated in all four categories.
On the Twentieth Century: John Cullum as Oscar Jaffee, Madeline Kahn as Lily Garland, Kevin Kline as Bruce Granit and Imogene Coca as Letitia Primrose.
Hamilton: Lin-Manuel Miranda as Alexander Hamilton, Leslie Odom, Jr. as Aaron Burr, Phillipa Soo as Elizabeth Schuyler Hamilton, Renée Elise Goldsberry as Angelica Schuyler Church, Jonathan Groff as King George III, Daveed Diggs as the Marquis de Lafayette / Thomas Jefferson and Christopher Jackson as George Washington.
What other shows received nominations in all 4 acting categories (be they plays or musicals)?
"Contentment, it seems, simply happens. It appears accompanied by no bravos and no tears."
Drowsy Chaperone had Bob Martin as a leading actor, Sutton Foster as a leading actress, Danny Burstein as a featured actor and Beth Leavel as a featured actress.
MUSICALS: Goodtime Charley (1975), Movin' Out (2003), Company (1971), Funny Girl (1964), Applause (1970), She Loves Me (1994), My One and Only (1983), Jerome Robbins' Broadway (1989), The Mystery of Edwin Drood (1986), Steel Pier (1997), Grand Hotel (1990), Passion (1994), Cabaret (1967), Promises, Promises (1969), Raisin (1974), Thoroughly Modern Millie (2002), Me and My Girl (1987), A Little Night Music (1973), Show Boat (1995), Damn Yankees (1956), Jamaica (1958.).
PLAYS: Separate Tables (1957), Vanya and Sonia and Masha and Spike (2013), King Hedley II (2001), Indiscretions (1995), Heartbreak House (1984).
Also - I think a lot of people were sharing that picture on social media of the seven hamilton nominees saying it was the first time that had ever happened in history, but Jerome Robbins' Broadway already did it in 1989 (Charlotte d'Amboise, Debbie Shapiro Gravitte, Faith Prince, Jane Lanier, Jason Alexander, Robert La Fosse, and Scott Wise). Not sure if someone had already pointed that out. (And, technically, Billy Elliot had 7 nominees, though of course the 3 billy elliots shared a single nomination, so that doesn't really count.)
I always forget the bizarre bit of trivia that the Weisslers forgot to petition for Joel Grey to be moved to the Featured Actor category for the CHICAGO revival, as I always assume that he got nominated for Featured Actor for the show.
"Some people can thrive and bloom living life in a living room, that's perfect for some people of one hundred and five. But I at least gotta try, when I think of all the sights that I gotta see, all the places I gotta play, all the things that I gotta be at"