Recent experiments involving heavy-ion collisions of isotopes 96Zr and 96Ru have revealed that initial nuclear deformation and neutron skin thickness considerably influence observables such as particle flow and multiplicity distributions in the final collision states.Covariant density functional theory—a microscopic nuclear structure model—uses one uniform ef-fective interaction to self-consistently describe nuclear ground-state structures such as shapes and neutron skin thicknesses.The beyond mean-field methods extended according to the covariant density functional theory have been successfully em-ployed to investigate the spectroscopic properties of low-lying collective excitations;these advanced approaches establish microscopic connections between experimental spectra and intrinsic deformations.In contemporary studies,experimental spectra and investigations using nuclear structure models suggest the potential coexistence of triaxial and octupole shapes in 96Zr.Herein,we introduce the multidimensionally-constrained covariant density functional theory,which breaks axial and spatial reflection symmetries,along with its beyond mean-field approach.Next,we examine the shapes and neu-tron skin thicknesses of 96Zr and 96Ru within mean field approximation.Finally,we investigate the beyond mean field corrections to the low-lying states of 96Zr and96Ru within a multidimensional deformation space.