Abstract Triple (or tribrachial) flames propagate through mixtures faster than the premixed laminar flame speed due to streamline divergence ahead of the flame base that decelerates the flow into the leading edge of the flame. When multiple triple flames are in close proximity, the bulk propagation speed of the structure can be even faster due to additional streamline divergence. Turbulent flames in partially-premixed conditions can encounter these situations, where multiple stoichiometric crossing are in close proximity, leading to multiple interacting triple flames being formed. Propagation speeds of the flame structure with respect the bulk flow for individual triple flames have been well characterized in previous studies, and the local flame speed of interacting triple flames have been reported; however, characterization of the propagation speed for the overall flame structure of interacting triple flame speeds has not been reported. The present work utilizes a laminar five slot burner, which allows both the concentration gradients and stoichiometric separation distance of two interacting triple flames to be varied. The bulk propagation speed of the multiple edge flames has been characterized as a function of the distance between the flame bases (or stoichiometric locations) and the local flame curvatures in order to better understand the conditions which lead to larger streamline divergence and faster propagation speeds. Interaction between multiple edge flames has been found to play an essential role in this propagation speed. Interacting edge flame speeds were modeled by modifying the relationship for single triple flame propagation speed with an added term for the interaction between the two flames to account for the increased effective divergence.