Multiple high-spin band structure in 164 Er

$^{164}\mathrm{Er}$ high-spin states were studied via the $^{160}\mathrm{Gd}(^{9}\mathrm{Be},5n)$ reaction at 59-MeV beam energy. We find significant population of three new rotational bands in addition to higher-spin levels of the previously known $\ensuremath{\gamma}$-vibrational band. In most cases the spins of the levels were established by angular distribution measurements, and some parities were established by linear polarization measurements on interband transitions. Two odd-parity bands with both even- and odd-spin states begin with the previously reported ${5}^{\ensuremath{-}}$ (1664 keV) and ${7}^{\ensuremath{-}}$ (1985 keV) levels and extend to levels of spin 22 (5350 keV) and 13 (3351 keV), respectively. These two bands exhibit markedly different moments of inertia. The third band is of unknown parity and has a likely even-spin sequence extending from a level of spin 8 (2091 keV) to a possible spin-22 level (5678 keV). The even-spin sequence of the $\ensuremath{\gamma}$ band extends to a spin-14 level (3267 keV) and exhibits a backbend at the ${10}^{+}$ level to a new ${12}^{+}$' level of the previously established even-spin even-parity yrast band. The odd-spin sequence backbends at spin 13, and extends to a possible spin-19 level at 4588 keV, thereby providing evidence for an odd-spin even-parity yrast band some 500 keV higher in energy than its even-spin counterpart.