Additional current pulses get injected into the lightning channel from branches and/or from successive reflections within struck Tall Grounded Objects (TGOs). These pulses termed here as ”secondary current waves/pulses“ affect the lightning Electro-Magnetic Fields (EMFs). With regard to these, an important question arises on whether or not these pulses get reflected at the main wavefront and there seems to be uncertainty in the pertinent literature. A particular case involving only the first ground end reflection from a struck TGO has been fully dealt in our earlier work. However, the same for subsequent reflections from TGO and that for the current fed by the branches were not dealt and this forms the main goal of present work. As the main objective is to ascertain the status of these secondary current pulses after they have reached the main wavefront, dynamics at the point of injection assumes lesser importance. In view of this, a lumped voltage source is employed for the injection of secondary current pulses at appropriate time instants. The main stroke evolution is emulated by a macroscopic physical model, which was developed in our earlier work. Investigation showed that these secondary pulses merge with the main wavefront without any sign of reflection whatsoever. Analysis showed that the spatial dynamic resistance/conductance profile at the main wavefront is basically responsible for the same with distributed source providing additional support. These findings are in line with the observations made in our earlier work for the first ground end reflected current.