Single band-edge states can trap light and function as high-quality optical feedback for microscale lasers and nanolasers. However, access to more than a single band-edge mode for nanolasing has not been possible because of limited cavity designs. Here, we describe how plasmonic superlattices-finite-arrays of nanoparticles (patches) grouped into microscale arrays-can support multiple band-edge modes capable of multi-modal nanolasing at programmed emission wavelengths and with large mode spacings. Different lasing modes show distinct input-output light behaviour and decay dynamics that can be tailored by nanoparticle size. By modelling the superlattice nanolasers with a four-level gain system and a time-domain approach, we reveal that the accumulation of population inversion at plasmonic hot spots can be spatially modulated by the diffractive coupling order of the patches. Moreover, we show that symmetry-broken superlattices can sustain switchable nanolasing between a single mode and multiple modes.