The supplementary eye field (SEF) is a region within medial frontal cortex that integrates complex visuospatial information and controls eye-head gaze shifts. Here, we test if the SEF encodes desired gaze directions in a simple retinal (eye-centered) frame, such as the superior colliculus, or in some other, more complex frame. We electrically stimulated 55 SEF sites in two head-unrestrained monkeys to evoke 3D eye-head gaze shifts and then mathematically rotated these trajectories into various reference frames. Each stimulation site specified a specific spatial goal when plotted in its intrinsic frame. These intrinsic frames varied site by site, in a continuum from eye-, to head-, to space/body-centered coding schemes. This variety of coding schemes provides the SEF with a unique potential for implementing arbitrary reference frame transformations.