The dog clutch offers advantages in mass and efficiency, but faces challenges in mismatch speed synchronization, which affects its shiftability. Face impact between dog teeth also reduces its lifespan. Our previous work introduced the kinematical shiftability condition that ensures impact-free gearshift but had limitations due to analysis assumptions. This study eliminates those assumptions, but uses a similar approach. Based on our previous work for dog clutch engagement dynamics, we develop the dynamical shiftability condition. Validation with full dog clutch dynamics showed an agreement. Employing another previous work that introduced shiftability map and parametric study method, we study system parameters impact on shiftability but based on the dynamical shiftability condition.