One approach for improving lithium transference in electrolytes is through the use of bulky multivalent anions. We have studied a multivalent salt containing a bulky star-shaped anion with a polyhedral oligomeric silsesquioxane (POSS) center and lithium counterions dissolved in a solvent. The charge on each anion, z-, is equal to -20. The self-diffusion coefficients of all species were measured by pulsed field gradient NMR (PFG-NMR). As expected, anion diffusion was significantly slower than cation diffusion. An approximate transference number, also referred to as the current fraction (measured by Bruce, Vincent and Watanabe method), was higher than those expected from PFG-NMR. However, the rigorously defined cation transference number with respect to the solvent velocity measured by electrophoretic NMR was negative at all salt concentrations. In contrast, the approximate transference numbers based on PFG-NMR and current fractions are always positive, as expected. The discrepancy between these three independent approaches for characterizing lithium transference suggests the presence of complex cation-anion interactions in solution. It is evident that the slow self-diffusion of bulky multivalent anions does not necessarily lead to an improvement of lithium transference.