© 2015 American Physical Society. Excited states in Lu167 were populated in the Sb123(Ca48,4n) reaction at 203 MeV and decay γ rays measured using the Gammasphere spectrometer array. Two triaxial strongly deformed bands were identified previously and interpreted as zero- and one-phonon wobbling excitations. As a result of more extensive band search, the level scheme has been considerably extended to include ten new rotational bands and some 630γ-ray transitions. A number of interband linking transitions were revealed, so that all but two bands could be connected with each other. Configurations are proposed for all new bands based on measured observables, with the help of cranked shell model calculations. A γ-ray sequence, previously suggested as a triaxial strongly deformed band based on quasiparticle excitations coexisting with the wobbling excitation in the triaxial potential well, has now been determined to be a signature partner of a coupled band, associated with a normal deformed five-quasiparticle configuration. The possibility of two new bands being associated with triaxial deformation is discussed.