There must be at least 17 people in the whole U.K. that haven't played in Deep Purple, Rainbow and Black Sabbath
But not a single person has played in all three bands! Well, Ian Gillan came close. He was invited to join Rainbow after Dio left. And wisely declined. To then join Sabbath as a replacement for, errrm, Dio.
Coverdale was invited to join Black Sabbath and Rainbow too. Also by MSG and Uriah Heep.
Heck, even "Arnold from Liverpool" has played with DP!