I just had an interesting discussion with one of my students. He came up to me and said: "I really like Vinnie Colaiuta. He is an amazing drummer. Is it possible to sound like him?" My advice for him was quite direct: it’s not really possible to sound like anyone else but yourself, but studying your idols gives you the whole new perspective. I’d start with copying some of his licks (phrases) and ideas and see where it leads you. There are a lot of transcriptions available, and I like transcribing for my students as well.
Let's talk a bit about styles of music. For example: there are some great rock drummers, but they can't really play other styles, such as jazz. And vice versa. Vinnie Coulaita is a unique musician. What really makes him so special is the ability to play all different styles of music. He can play jazz, rock, fusion, latin, etc. He even recorded an album with a heavy metal band Megadeth. A couple of words about his technique. If you watch him play, it looks very natural and effortless. A big part of it is his use of Moeller technique. A lot of drummers (including myself) had to work on Moeller technique quite a lot to make it feel natural. According to a wonderful drummer and teacher Jim Chapin, Vinnie Colaiuta always played using Moeller technique and didn't have to work on at all.