  Shell model and interacting boson model spaces admit multiple
$SU^{(\alpha)}(3)$ algebras generating the same rotational spectra but
different $E2$ decay properties, depending on the phases ${\alpha}$ in the
quadrupole generator. In the ground ($g$) $K=0^+$ bands in nuclei this is
demonstrated recently using systems with nucleons in a single oscillator shell
[Kota, Sahu and Srivastava, Bulg. J. Phys. {\bf 46}, 313 (2019); Eur. Phys. J.
Special Topics {\bf 229}, 2389 (2020)]. Going beyond these preliminary studies,
results are presented here for $E2$ decay properties of $\beta$ and $\gamma$
bands members, as generated by multiple $SU(3)$ algebras, using $sdg$IBM and
$sdgi$IBM examples. In addition, results are presented for the $E2$ and $M1$
decay properties of the levels of the $1^+$ scissors band in heavy nuclei using
$sdg$IBM-2 and $sdgi$IBM-2. The scissors $1^+$ band properties are also studied
using a shell model example with six protons in $(pf)$ shell and twelve
neutrons in $(sdg)$ shell. These results establish that: (i) with multiple
$SU(3)$ algebras, it is possible to have rotational bands with very weak $E2$
strengths among the levels where normally one expects strong strengths; (ii)
$E2$ decay of the levels of $\beta$ and $\gamma$ bands to the ground band are
quite different for some of the $SU^{(\alpha)}(3)$ algebras with strong
dependence on ${\alpha}$; (iii) it is possible to have the scissors $1^+$ band
with the $E2$ and $M1$ decay of the low-lying levels of this band to the $g$
band are strong or weak depending on $\alpha$.
