  We identify different schemes to enhance the violation of Leggett-Garg
inequalities in open many-body systems. Considering a nonequilibrium
archetypical setup of quantum transport, we show that particle interactions
control the direction and amplitude of maximal violation and that in the
strongly-interacting and strongly-driven regime bulk dephasing enhances the
violation. Through an analytical study of a minimal model, we unravel the basic
ingredients to explain this decoherence-enhanced quantumness, illustrating that
such an effect emerges in a wide variety of systems.
