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Several families of one-point interactions are derived from the systemconsisting of two and three $\delta$-potentials which are regularized bypiecewise constant functions. In physical terms such an approximating systemrepresents two or three extremely thin layers separated by some distance. Thetwo-scale squeezing of this heterostructure to one point as both the width of$\delta$-approximating functions and the distance between these functionssimultaneously tend to zero is studied using the power parameterization througha squeezing parameter $\varepsilon \to 0$, so that the intensity of each$\delta$-potential is $c_j =a_j \varepsilon^{1-\mu}$, $a_j \in {\mathbb{R}}$,$j=1,2,3$, the width of each layer $l =\varepsilon$ and the distance betweenthe layers $r = c\varepsilon^\tau$, $c >0$. It is shown that at some values ofintensities $a_1$, $a_2$ and $a_3$, the transmission across the limit pointinteractions is non-zero, whereas outside these (resonance) values theone-point interactions are opaque splitting the system at the point ofsingularity into two independent subsystems. Within the interval $1 < \mu < 2$,the resonance sets consist of two curves on the $(a_1,a_2)$-plane and threedisconnected surfaces in the $(a_1,a_2,a_3)$-space. While approaching theparameter $\mu $ to the critical value $\mu =2$, three types of splitting thesesets into countable families of resonance curves and surfaces are observed.

Families of one-point interactions resulting from the squeezing limit of the sum of two- and three-delta-like potentials