We show experimentally that the interaction of two multifilamenting beams in fused silica with incidence angles up to a few degrees results in an increase in the symmetry of the continuum emission from D2 to C∞ around the axis of symmetry between the two beams. We observe an intense white disk between the locations of the individual conical emission patterns, reducing the conical emission in each of them. We attribute this behavior to an enhanced self-phase modulation in the interference region between the two beams. This frequency conversion depletes by more than 40% the energy initially available in the photon bath to feed filaments.