There are many more examples beyond Hitchcock and DeMille. A third was Leo McCarey, who directed "Love Affair" in 1939 and remade it as "An Affair to Remember" in 1957 (in fact, he even used the same screenplay, although there are a few amendments). A fourth was John Ford, who made "Judge Priest" with Will Rogers on a fairly low budget in 1934 and then remade it (with a new script, so that he could include a scene of the judge stopping a lynching) as "The Sun Shines Bright" in 1953. A fifth (and perhaps more interesting) one was Howard Hawks, who made "Rio Bravo" in 1959 (as a response to "High Noon"), but then, while shooting a different film, "El Dorado", with a script by one of the same writers, Leigh Brackett, decided to turn the second act of the movie into a remake of "Rio Bravo", except with a few twists mandated by the new first act, such as John Wayne being transitioned from the sheriff to a gunfighter and the role of the drunken deputy (Dean Martin) now transformed into a drunken sheriff (Robert Mitchum). Finally, a sixth was Frank Capra, who did it twice: remaking his 1933 "Lady for a Day" as 1961's "Pocketful of Miracles" and his 1934 "Broadway Bill" as 1950's "Riding High".
And then there are the remakes because the original was shot in a different language, such as George Sluizer's "The Vanishing" (1988 in Dutch ("Spoorloos"), 1993 in English), Michael Haneke's "Funny Games" (1997 in German, 2007 in English), and Takashi Shimizu's "Ju-On: The Grudge" (2002 in Japanese, 2004 in English as just "The Grudge"). And like DeMille, Abel Gance remade "J'accuse!" as a "talkie" in 1938 because his 1919 original was a silent, and Yasujiro Ozu remade his 1934 silent "A Story of Floating Weeds" as a color talkie in 1959 as "Floating Weeds". And then there is Michael Mann, who did "L.A. Takedown" as a TV movie in 1989 (it was a failed pilot) and then remade it as a big-budget feature film called "Heat" in 1995. Many more such examples exist.
So that gives us 12, and in searching for a link I found this article, which lists all of them except McCarey and Capra:
http://www.tasteofcinema.com/2018/10-directors-who-remade-their-own-films/
And then I found this article, which omits McCarey, Capra, Gance, Ozu, Ford, and Hawks but adds Ole Bornedal, Gela Babluani, and The Pang Brothers (all of whom redid their original foreign-language films in English), and the semi-sequel by Sam Raini of "Evil Dead"/"Evil Dead II".
https://www.denofgeek.com/movies/10-directors-who-remade-their-own-films/
That gets us up to 16, and we aren't even counting the directors who remade their shorts or student films into features (such as George Lucas's "THX 1138"). I expect that the real answer to this question depends on your definition of a remake.
