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Driven by rapid growth in wireless demand, spectrum sharing has recently been the focus of extensive research. A common concern is how to address coexistence-related interference, especially when the involved systems operate under different protocols. In this paper, we outline a framework for exploiting full-duplex (FD) capabilities to support coexistence in a heterogeneous spectrum sharing environment. Besides the traditional simultaneous transmission/reception (STAR) mode, we advocate a simultaneous transmission and sensing (STAS) mode that allows for rapid interference detection and migration to other channels. Specific examples of LTE-U/Wi-Fi coexistence and opportunistic (primary/secondary) access are used to demonstrate the idea.