Jack co-exists with co-owned Classic Hits stations in Los Angeles (KCBS-FM and KRTH, both owned by Entercom) and Dallas (KJKK and KLUV, again under Entercom ownership).
Yes, they share some songs. But I think Jack is aimed more at people who had been listening to Album Rock and Alternative Rock stations in their youth. Classic Hits is more for those who listened to Top 40 stations.
Jack has only a sarcastic voice for its image, while Classic Hits stations rely on very foreground DJs, many of whom had previously been popular Top 40 DJs in their markets.
So if programmed correctly, I think an owner can have both types of stations in the same market.