Divetech at Cobalt Coast does extensive tech diving and training, including CCR. If you're talking about regular, more advanced sites, many operators would fit the bill. There are many dive sites for more experienced divers off Grand Cayman. I have 8 visits and 142 dives off Grand Cayman since 1997 and see and find new things each time. The deep wall diving is dazzling. Perhaps Wood's Dive Guide to the Cayman Islands or Lonely Planet's Diving & Snorkeling Cayman Islands would help you choose some sites before your visit. Many operators could tailor sites to fit the experience of your group. I have had good personal experience with Divetech, Cayman Diving School and Wall to Wall Diving. Best of luck, enjoy your visit to Grand Cayman.
Good diving, Craig