We show that the theoretical description of the spontaneous evolution of an epitaxially growing surface towards self-organised structures, changes qualitatively when the simultaneous presence of several chemical species is taken into account. In the framework of a two-particle model studied by Monte-Carlo simulations we prove that a growing surface can exhibit step meandering, step bunching and mounding in different growth regimes, assuming only positive Ehrlich-Schwoebel step-edge barrier.