Whether the evolutionary dynamics of one group of organisms influence that of another group of organisms over the vast timescale of the geological record is a difficult question to tackle. This is not least because multiple factors can influence or mask the effects of potential driving forces on evolutionary dynamics of the focal group. Here, we show how an approach amenable to causality inference for time series, linear stochastic differential equations (SDEs), can be used in a multivariate fashion to shed light on driving forces of diversification dynamics across the Phanerozoic. Using a new, enhanced stepwise search algorithm, we searched through hundreds of models to converge on a model that best describes the dynamic relationships that drove brachiopod and bivalve diversification rates. Using this multivariate framework, we characterized a slow process (half-life of c. 42 Myr) that drove brachiopod extinction. This slow process has yet to be identified from the geological record. Using our new framework for analyzing multiple linear SDEs, we also corroborate our previous findings that bivalve extinction drove brachiopod origination in the sense that brachiopods tended to diversify at a greater rate when bivalves were removed from the system. It is also very likely that bivalves “self-regulate” in the sense that bivalve extinctions also paved the way for higher bivalve origination rates. Multivariate linear SDEs as we presented them here are likely useful for studying other dynamic systems whose signatures are preserved in the paleontological record.