When multilayer films are built up with polycations and polyanions, their thickness can grow either linearly or exponentially with the number of deposited layer pairs, depending for example on the nature of the polyelectrolytes used. We investigate in the present work the construction of a film using a binary mixture of polyanions as polyanion solution. The two anionic components are chosen such that one of them causes the film to grow linearly while the other causes the film to grow exponentially. It is observed that a mixture of both components leads to a hybrid growth law, depending on its composition. At the beginning of the construction, the thickness of the film increases exponentially with the number of deposited bilayers. Once a given thickness is reached, one observes the crossover to a linear growth regime. This finding is discussed on the basis of the diffusion coefficients of the polyanions that are assumed to diffuse "in" and "out" of the film.