Here we present a coherent pulse stacking approach for upscaling the energy of a solid-state femtosecond chirped pulse amplifier. We demonstrate pulse splitting into four replicas, amplification in a burst-mode regenerative Yb:CaF2 amplifier, designed to overcome intracavity optical damage by colliding pulse replicas, and coherent combining into a single millijoule level pulse. The thresholds of pulse-burst-induced damage of optical elements are experimentally investigated. The scheme allows achieving an enhancement factor of 2.62 using a single-stage stacker cavity and, potentially, much higher enhancement factors using cascaded stacking.