The purpose of this paper is to show that molecularly-driven double-diffusive intrusions can produce significant lateral and vertical double-diffusive mixing even when the initial temperature and salinity are both stably stratified in the vertical. Assuming uniform density-compensated horizontal gradients and periodic disturbances, three-dimensional direct numerical simulations (DNS) for the fastest growing intrusion show that the latter equilibrates due to the generation of salt fingers which reduce the driving buoyancy pressure gradient. The DNS also provided statistical data for a new parameterization of the salt finger fluxes which includes the effects of shear and variable vertical gradients. This parameterization makes it feasible to numerically investigate the subharmonic instabilities of the equilibrium DNS solution. Linearized calculations with parameterized salt fingers show that the vertical and horizontal wavelength of the fastest growing secondary instability are approximately three and fourteen times that of the primary intrusion. Nonlinear simulations show that the equilibrium lateral and vertical double-diffusive fluxes of the secondary mode are an order of magnitude larger than those of the primary intrusion. Numerically determined dependences of the intrusion lateral velocity on the vertical wavelength are compared to previous numerical and experimental work.