Complex nanoemulsions, comprising multiphase nanoscale droplets, hold considerable potential advantages as vehicles for encapsulation and delivery as well as templates for nanoparticle synthesis. Although methods exist to controllably produce complex emulsions on the microscale, very few methods exist to produce them on the nanoscale. Here, we examine a recently developed method involving a combination of high-energy emulsification with conventional cosurfactants to produce oil-water-oil (O/W/O) complex nanoemulsions. Specifically, we study in detail how the composition of conventional ethoxylated cosurfactants Span80 and Tween20 influences the morphology and structure of the resulting complex nanoemulsions in the water-cyclohexane system. Using a combination of small-angle neutron scattering and cryo-electron microscopy, we find that the cosurfactant composition controls the generation of complex droplet morphologies including core-shell and multicore-shell O/W/O nanodroplets, resulting in an effective state diagram for the selection of nanoemulsion morphology. Additionally, the cosurfactant composition can be used to control the thickness of the water shell contained within the complex nanodroplets. We hypothesize that this degree of control, despite the highly nonequilibrium nature of the nanoemulsions, is ultimately determined by a competition between the opposing spontaneous curvature of the two cosurfactants, which strongly influences the interfacial curvature of the nanodroplets as a result of their ultralow interfacial tension. This is supported by a correlation between cosurfactant compositions that produces complex nanoemulsions and those that produce homogeneous mixed micelles in equilibrium surfactant-cyclohexane solutions. Ultimately, we show that the formation of complex O/W/O nanoemulsions is weakly perturbed upon the addition of hydrophilic polymer precursors, facilitating their use as templates for the formation of polymer nanocapsules.