  Rotational $SU(3)$ algebraic symmetry continues to generate new results in
the shell model (SM). Interestingly, it is possible to have multiple $SU(3)$
algebras for nucleons occupying an oscillator shell $\eta$. Several different
aspects of the multiple $SU(3)$ algebras are investigated using shell model and
also deformed shell model based on Hartree-Fock single particle states with
nucleons in $sdg$ orbits giving four $SU(3)$ algebras. Results show that one of
the $SU(3)$ algebra generates prolate shapes, one oblate shape and the other
two also generate prolate shape but one of them gives quiet small quadrupole
moments for low-lying levels. These are inferred by using the standard form for
the electric quadrupole transition operator and using quadrupole moments and
$B(E2)$ values in the ground $K=0^+$ band in three different examples. Multiple
$SU(3)$ algebras extend to interacting boson model and using $sdg$IBM, the
structure of the four $SU(3)$ algebras in this model are studied by coherent
state analysis and asymptotic formulas for $E2$ matrix elements. The results
from $sdg$IBM further support the conclusions from the $sdg$ shell model
examples.
