The volume-realized volatility relationship has been extensively documented in the extant financial literature. However, minimal attention has been accorded to volume-realized skewness and volume-realized kurtosis relationships. Our insight in this paper is that these additional higher-order realized moments hold volume-dependent relationships that have been neglected. We sample 142 Australian stocks from 2003 to 2017 downloaded at 15-minute sampling-intervals from the TRTH/SIRCA database and compute their weekly and monthly realized high-order moments. We find that the volume proxy influences the signage of the ensuring volume-higher-order realized moment regression coefficients. We then attempt to relate our empirical findings to the three common volume-related hypotheses cited in the extant volume literature and conclude that the DOH (Difference of Opinion) hypothesis implicitly encompasses or nests both the MDH (Mixture of Distributions) and SIAH (Sequential Information Arrival) hypotheses. These two subtle but significant findings have yet to be reported in the extant volume or trading-related studies.