Laminar lifted edge flames stabilized above a five- exit slot burner are examined experimentally using particle imaging velocimetry and OH planar laser- induced fluorescence. In the present study, partially premixed methane and air are used to create a single lifted tribrachial flame that replicates many previous studies. Utilizing the same burner, two neighboring lifted tribrachial flames whose flow fields interact are also produced. This interaction results in a previously unknown bifurcation where two stable flame configurations are observed. For modest equivalence ratio gradients, the flow divergence around one flame edge pushes the other edge to an increased lift off height. The upper flame structure continues to impact the orientation and flow field around the lower flame. Global propagation velocities for the flame structure as a whole are greater than that for a single edge flame with the same equivalence ratio gradient. For very small equivalence ratio gradients, a chemical interaction between the edge flames is observed. The two edge flame structures eventually merge as the equivalence ratio gradient is reduced to a point approaching that of a fully premixed flame. These flame interactions may affect the stabilization of flame edges in turbulent flows where multiple stoichiometric points can exist in close proximity.