The growth of an arbitrary multicomponent non-Kossel crystal via the Burton-Cabrera-Frank mechanism is studied, considering the effect of advacancies and their recombination with adatoms on the surface. An analysis is carried out for two cases: growth due to vapours and growth due to chemical reactions. The analytical expressions are found for the rate of advancement of a group of equidistant steps and the crystal growth rate considering the properties of all the species involved in the growth process. Gallium nitride is used as an example to show that the effect is stronger at higher temperatures and in the presence of dopants that may increase the vacancy concentration. The impact of applied mechanical stress on the growth rate and mechanisms of its influence on the growth kinetics are discussed. It is demonstrated that the contribution of the vacancies to the total mass transfer depends on the type of applied stress. Tensile stresses increase the concentration of advacancies and total recombination rate, whereas compressive stresses lead to the opposite result. Some effects inherent to the multicomponent systems being considered are discussed.