- We study a generally covariant model with SSB of scale invariance where two measures of integration in the action enter: the standard and a new Φd4x, where Φ is a density built out of degrees of freedom independent of the metric. The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame, after SSB of scale invariance, the theory develops the exponential potential and, in general, non-linear kinetic term is generated as well. The scale symmetry does not allow the appearance of terms breaking the exponential shape of the potential that solves the problem of the flatness of the scalar field potential in the context of quintessential scenarios. Under normal laboratory conditions where the fermionic matter dominates, it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles which can be identified with known fermion families. It is automatically achieved that for two of them, fermion masses are constants, the energy-momentum tensor is canonical and the "fifth force" is absent. For the third family, a self-interaction appears as a result of SSB of scale invariance.