We introduce a continuous family of high order neural network models which solve the set selection problem: given a finite list of finite sets, find a set that intersects each of them in exactly one element. The additive model proposed earlier by Clark Jeffries belongs to this family. We study deformations of the additive model within our family in a case when 50% of its attracting equilibria do not correspond to answer sets of the problem. As a result, we show that the phase portrait of this model is structurally unstable. We describe deformations that admit only meaningful constant attractors.