Classical Lie symmetry analysis is proposed to get similarity reductions of a nonlinear (3+1)-modified Korteweg de Vries-Zakharov-Kuznetsov equation. The equation is often used to control the type of weakly nonlinear ion-acoustic waves in a homogeneous magnetised electron-positron plasma. In a magnetised plasma including some hot and cold ions, such waves exist. Some more general types of analytical solutions to the equation are derived in this article. Through their animation profiles, the dynamics of electrostatic potential indicate elastic single soliton to multi solitons, elastic multi solitons, kink to stationary, bell-shaped to asymptotic. The solutions are confirmed by comparing the existing results.