The mechanism of nonlinear harmonic generation in the exponential gain regime, which is driven by bunching at the fundamental wavelength, may provide a path toward both enhancing and extending the usefulness of an x-ray free-electron laser (FEL) facility. Related "exotic" generation schemes, which exploit properties of harmonic production in various undulator topologies, have been discussed both in the past and more recently. Using three different numerical simulation codes, we explore the possible utility of such schemes (e.g., harmonic "afterburners" and biharmonic undulators) at future light source facilities.