  Families of one-point interactions are derived from the system consisting of
regularized two- and three-delta potentials using different paths of the
convergence of corresponding transmission matrices in the squeezing limit. This
limit is controlled by the relative rate of shrinking the width of delta-like
functions and the distance between these functions using the power
parameterization: width $l =\varepsilon^{\mu -1}$, $\mu \in [2,\, \infty]$ (for
width) and $r = \varepsilon^\tau$, $\tau \in [1,\, \infty]$ (for distance). It
is shown that at some values of real coefficients (intensities $a_1$, $a_2$ and
$a_3$) at the delta potentials, the transmission across the limit point
interactions is non-zero, whereas outside these (resonance) values the
one-point interactions are opaque splitting the system at the point of
singularity into two independent subsystems. The resonance sets of intensities
at which a non-zero transmission occurs are proved to be of four types
depending on the way of squeezing the regularized system to one point. In its
turn, on these sets the limit one-point interactions are observed to be either
single- or multiple-resonant-tunnelling potentials also depending on the
squeezing way. In the two-delta case the resonance sets are curves on the
$(a_1,a_2)$-plane and surfaces in the $(a_1,a_2,a_3)$-space for the three-delta
system. A new phenomenon of furcation of single-valued resonance sets to
multi-valued ones is observed under approaching the parameter $\mu >2$ to the
value $\mu =2$.
