Cadillac’s 21st-century resurgence began with the first CTS-V (2004–07). Its mission was simple but ambitious: Go head-to-head with sedans from Mercedes-AMG, BMW’s M division, and Audi’s S/RS family.

The third-generation Cadillac CTS-V may have overshadowed the second-generation model with its 650 hp supercharged LT4 engine and quick-shifting eight-speed automatic transmission, but there’s still a ...