Yep, its called hot staging & was used on some of the Titans for example. Another even more conservative option is to ground start all your engines and then th

Yep, its called hot staging & was used on some of the Titans for example. Another even more conservative option is to ground start all your engines and then throw some of them away directly (original Atlas) or with a stage (R7/Soyuz). There are certainly some tradeoffs with this, such as making it impossible to use a proper altitude/vacuum optimized nozzle if all your engines are ground started.