It seems that most of the great players took a few years to settle in at the top. Pete won his first Slam in 1990 but he didn't win another one for 3 years, like Novak.
Those two are so far the only ones to do that, of those winning a lot of slams.
For Connors, 2nd slam was same year as 1st
For Borg, 2nd was the year after the 1st. Same for Wilander, Lendl, Becker, McEnroe, Federer, Nadal
For Agassi, 2nd was 2 years after the 1st. Same for Edberg.