We present the formulation of a new infinite family of self-consistent stellar models, designed to describe axisymmetric flat galaxies. The corresponding density–potential pair is obtained as a superposition of members belonging to the generalized Kalnajs family, by imposing the condition that the density can be expressed as a regular function of the gravitational potential, in order to derive analytically the corresponding equilibrium distribution functions (DFs). The resulting models are characterized by a well-behaved surface density, as in the case of generalized Kalnajs discs. Then, we present a study of the kinematical behaviour which reveals, in some particular cases, a very satisfactory behaviour of the rotational curves (without the assumption of a dark matter halo). We also analyse the equatorial orbit's stability, and Poincaré surfaces of section are performed for the three-dimensional orbits. Finally, we obtain the corresponding equilibrium DFs, using the approaches introduced by Kalnajs and Dejonghe.