Extreme precipitation events (EPEs) have great socioeconomic impacts. The extratropical EPE is essentially a large-scale-convection coupled system. The large-scale adiabatic perturbations induce dynamically forced vertical motion and stimulate the development of deep convection by destabilizing the atmospheric stratification. The latent heating released by convection, in turn, drives further large-scale ascent by allowing air parcels to rise across surfaces of potential temperature. We use the quasi-geostrophic omega equation, with the diabatic heating term included, to develop a deeper understanding of its dynamics. Changes in precipitation extremes under climate change are societally important but subject to substantial uncertainty. While atmospheric moisture increases with warming, making extreme rain events heavier at a well-understood rate of 7%/K, a component associated with storm dynamics is much less well understood and can either amplify or reduce that moisture-driven intensification. This paper uses a novel idealized modeling framework to understand the coupling of these two components, simulating one real heavy rain event within perturbed climates. The dynamical component acts as a positive feedback amplifying the increased moisture-driven response, particularly for warmer climates. Our results highlight the importance of the cross-scale interactions between vertical motion and convection in constraining the responses of precipitation extremes to climate change.