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We analyze the sensitivity of fixed-target experiments to sub-GeV thermal relic dark matter models, accounting for variations in both mediator and dark matter mass, and including dark matter production through both on- and off-shell mediators. It is commonly thought that the sensitivity of such experiments is predicated on the existence of an on-shell mediator that is produced and then decays to dark matter. While accelerators do provide a unique opportunity to probe the mediator directly, our analysis demonstrates that their sensitivity extends beyond this commonly discussed regime. In particular, we provide sensitivity calculations that extend into both the effective field theory regime where the mediator is much heavier than the dark matter and the regime of an off-shell mediator lighter than a dark matter particle-antiparticle pair. Our calculations also elucidate the resonance regime, making it clear that all but a fine-tuned region of thermal freeze-out parameter space for a range of simple models is well covered.