The multiconfigurational time-dependent Hartree (MCTDH) approach uses optimized sets of time-dependent basis functions, called single-particle functions, to represent multidimensional wavefunctions and thereby facilitates efficient multidimensional quantum dynamics studies. The single-particle function bases are usually optimized for a single wavefunction. Here, an approach is studied which utilizes a common single-particle function basis to represent several wavefunctions simultaneously, i.e., the single-particle function basis is constructed to result in an optimized averaged description of a number of wavefunctions. The approach can favorably be used to obtain eigenstates of Hamiltonians or to represent thermal ensembles. Test calculations studying the vibrational states of CH(3) and the thermal rate constant of the H+CH(4)-->H(2)+CH(3) reaction are presented. It is found that the required size of the single-particle functions basis does not increase when the number of wavefunctions described simultaneously is increased. As a consequence, the new approach offers an increased efficiency, e.g., for MCTDH rate constant calculations.