Dynamic interaction of multiple plumes is commonly observed in the natural and built environment. When multiple plumes are discharging close to each other, the plume induced flow and pressure field leads to a change in the trajectory and mixing characteristics of adjacent plumes in proximity. A general semi-analytical model for the dynamic interaction of multiple plumes in stagnant ambient is proposed. The flow field induced by plumes is computed by a distribution of point sinks with strength equal to the entrainment per unit length along the unknown plume trajectory. The plume flow is determined by an iterative solution of an integral jet model accounting for dynamic pressure and momentum flux changes. Model predictions of the merging height of a pair of turbulent plumes of equal and unequal buoyancy flux are in good agreement with the experiments of Kaye & Linden (2004).