The nucleus 166Hf has been populated by the reaction 96Zr(74Ge,4n) using a beam energy of 310MeV. γ-rays were detected with the EUROBALL III detector array. Fourteen new normal-deformed rotational bands, of which six form coupled pairs, have been observed in 166Hf. Four previously known bands have been extended to considerably higher spin, and configurations of the new bands are proposed. Two different bands have been assigned configurations involving the same orbitals at high spin. The two coupling schemes, deformation and rotation alignment, are discussed in connection with this new observation, which calls for a formulation of co-existing coupling schemes in six-quasiparticle structures involving the same orbitals at high spin.