The projected shell model is used to study the multi-quasiparticle and collective excitations of ¹⁷⁸Hf. With an axially symmetric basis, the spin-16 isomer at 2.4 MeV appears to be well separated in energy/spin space from other configurations. However, projected energy surface calculations suggest that ¹⁷⁸Hf has significant softness to axially asymmetric shapes, which can strongly modify the level distribution. The implications for photodeexcitation of the isomer are discussed.