We investigate the occurrence of Majorana modes in semiconductor quantum wires in close proximity with a superconductor and when both Rashba interaction and magnetic field are present. We consider long, but finite,multibandwires(namely,planarwireswithdimensionsLx ≫Ly).Ourresultsdemonstratethatinterband mixing coming from the Rashba spin-orbit term hybridizes Majorana pairs originating from different transverse modes while simultaneously closing the effective gap. Consequently, multiple Majorana modes do not coexist in general. On the contrary, Majorana physics is robust provided that only one single transverse mode contributes to a Majorana pair. Finally, we analyze the robustness of Majorana physics with respect to magnetic orbital effects.