Continental lithosphere extension results in complex basin types with differing structural styles, subsidence, thermal histories, and melt production. Many studies have examined the role of initial rheological layering, geothermal gradients, and extension rates during a single rifting event. This approach neglects the tectonic history of many basins that are marked by multiple rifting events. Here we address the role of repeated extension on long‐term lithospheric strain modes and the resulting basins, highlighting cases most affected by previous rifting events. We use numerical models of a lithosphere undergoing two rifting events of differing extension rates and separated by cooling, to show the effect of early events on subsequent evolution. The combination of boundary displacement velocity in both events leads to the formation of various rift basin types, ranging from narrow to wide to hyperextended and with variation of subsidence patterns, degrees of symmetry, and melt yield. We show that basin type, subsidence, and melt production might be strongly affected by previous rifting events, illustrating cases in which the previous rifting history cannot be neglected. Our models reproduce the first‐order features of Earth's sedimentary basins and propose a classification to guide the interpretation of extensional basins and their evolution.

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