Maybe starting with No- Hitters a catcher has?
Carlos Ruiz had 4 for the Phillies, two with Halladay, a combined and one with Hamels
Jason Varitek also had 4, with Nomo, Lowe, Bucholz and Lester.
If I remember it right one was followed by a one hitter with Schilling who said the hit came on the only pitch he shook off.
Lots, including Berra with 3
https://www.mlb.com/news/catchers-wi...ost-no-hitters
What makes it a more difficult comparison, is the differing quality of the pitchers, for example Variteks were generally with decent but newish pitchers who went on to be good but not always great while Ruiz had Halladay for two of them.
Berra and other catchers before the advent of teams having 100% film availability and ways to look at the data to get a better idea of a hitters tendencies are probably more impressive.