  Symmetries are known to play an important role in the low lying level
structure of Sn isotopes, mostly in terms of the seniority and generalized
seniority schemes. In this paper, we revisit the multi-j generalized seniority
approach for the first excited $2^+$ and $3^-$ states in the Cd ($Z=48$), Sn
($Z=50$) and Te ($Z=52$) isotopes, where the Cd and Te isotopes represent
two-proton hole and two-proton particle nuclei, thus involving both kind of
particles (protons and neutrons) in contrast to Sn isotopes. Interestingly, the
approach based on neutron valence space alone is able to explain the B(E2) and
B(E3) trends respectively for the $2^+$ and $3^-$ states in all the three Cd,
Sn and Te isotopes. The new results on the inverted parabolic behavior of B(E3)
values in Cd and Te isotopes are understood in a manner identical to that of Sn
isotopes by using the generalized seniority scheme. No shell quenching is
supported by these calculations; hence, the neutron magic numbers, $N=50$ and
$N=82$, remain robust in these isotopic chains. It is quite surprising that the
generalized seniority continues to be reasonably successful away from the
semi-magic region, thus providing a unifying view of the $2^+$ and $3^-$
states.
