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Shell model and interacting boson model spaces admit multiple$SU^{(\alpha)}(3)$ algebras generating the same rotational spectra butdifferent $E2$ decay properties, depending on the phases ${\alpha}$ in thequadrupole generator. In the ground ($g$) $K=0^+$ bands in nuclei this isdemonstrated 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 studiedusing a shell model example with six protons in $(pf)$ shell and twelveneutrons 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 arequite different for some of the $SU^{(\alpha)}(3)$ algebras with strongdependence on ${\alpha}$; (iii) it is possible to have the scissors $1^+$ bandwith the $E2$ and $M1$ decay of the low-lying levels of this band to the $g$band are strong or weak depending on $\alpha$.

Multiple $SU(3)$ algebras in interacting boson model and shell model: Results for $(\beta ,\gamma$) bands and scissors $1^+$ band