We investigate the plausibility of some models emerging from an algorithm devised to generate a one-parameter family of interior solutions for the Einstein equations. It is explored how their physical variables change as the family-parameter varies. The models studied correspond to anisotropic spherical matter configurations having a non local equation of state. This particular type of equation of state with no causality problems provides, at a given point, the radial pressure not only as a function of the density but as a functional of the enclosed matter distribution. We have found that there are several model-independent tendencies as the parameter increases: the equation of state tends to be stiffer and the total mass becomes half of its external radius. Profiting from the concept of cracking of materials in General Relativity, we obtain that those models become more stable as the family parameter increases.