<p>An extended version of the interacting boson model, which includes some high-rank symmetry-conserving terms, has been used to investigate the rotational bands of deformed nuclei whose gamma and beta bands are displaced. The theoretical framework of the considered Hamiltonian, together with the details of the expectation values of these new terms, is presented in such Elliott states where the second- and third-order terms are diagonal. The predicted results for the gamma and beta bands are different, and this extension removes the degeneracy of the normal SU(3) formalism. To investigate the advantages of this extended Hamiltonian for the exact description of the energy spectra, we considered the ¹⁵⁸Gd, ^158,162Dy, ¹⁶⁸Yb, and ¹⁷⁸Hf nuclei and compared our results for the different levels of the ground, gamma, and beta bands with their experimental counterparts and also the predictions of partial dynamical symmetry framework. Our results show that, the best alignment between theoretical and experimental data is achieved for the levels belonging to the beta band in all of the considered nuclei. We also investigated the variation of the averaged standard deviations of our results relative to the experimental quadrupole deformation and neutron numbers and observed a significant dependence between them.</p>