This is actually one I'm ready to answer, right at my finger tips because I've been thinking about this for various reasons, but, yes, there are many examples of this in Cardinals history. Especially if you include Walker in the mix because the majority of his career was definitely not in St. Louis, so you've got like Dazzy Vance that you could put with the 1930s teams. Or, Cepeda which you could easily include with that 1960s group.
In Cepeda's MVP season of 1967, that team had Lou Brock, Bob Gibson, Cepeda, and Stave Carlton. Also on that roster -- Curt Flood and Roger Maris. Both of them have claims to Hall of Fame consideration. The manager was HOFer Red Schoendienst, the GM Stan Musial, and the catcher is in the Hall of Fame for broadcasting, Tim McCarver.
In the 1920s -- you had Frisch, Bottomley, Haines, and Hafey, not to mention Hornsby before Frisch. In the 1930s -- Dean, Medwick, Durocher, Mize, and a handful of others who made their names elsewhere like Vance. In the 1940s -- there was Slaugher, Musial, and Schoendienst who had long careers together in the same lineup, and Terry Moore gets some attention as one of the best center fielders who isn't in the Hall. In the 1960-1970s, there is the overlap of Gibson, Brock, Carlton, and now Ted Simmons, to go along with deserving third baseman Ken Boyer.