Models of adaptive radiation through intraspecific competition have attracted mounting attention. Here we show how extending such models in a simple manner, by including a quantitative trait under weak directional selection, naturally leads to rich macroevolutionary patterns involving recurrent adaptive radiations and extinctions. Extensive tests demonstrate the robustness of this finding to a wide range of variations in model assumptions. In particular, recurrent adaptive radiations and extinctions readily unfold both for asexual and for sexual populations. Since the mechanisms driving the investigated processes of endogenous diversification result from generic geometric features of the underlying fitness landscapes--frequency-dependent disruptive selection in one trait and weak directional selection in another--the reported phenomena can be expected to occur in a wide variety of eco-evolutionary settings.