In the study of faint, extended sources at high resolving power, interferometry offers significant etendue advantages relative to conventional dispersive grating spectrometers. A Spatial Heterodyne Spectrometer (SHS) is a compact format two-beam interferometer that produces wavenumber dependent 2-D Fizeau fringe pattern from which an input spectrum can be obtained via a Fourier transform. The sampled bandpass of SHS is limited by the highest spatial frequency that can be sampled by the detector, which is typically less than 10 nm. This limitation has made these instruments useful primarily for studies of single emission line features or molecular bands. To date there have been few broadband implementations. We describe here continuing progress toward development of a broadband tunable SHS (TSHS) that is based on an all-reflective format where a single grating operates simultaneously as a beam-splitter, dispersive element, and beam combiner. The narrow spectral coverage of the TSHS is moved to different tuning wavenumbers by adjusting the angle of the pilot mirrors that guide the interfering beams through the optical path, thus slewing the acceptance band over a much broader spectral range. Our present effort involves a breadboard laboratory prototype of a secondgeneration TSHS in which we address several technical limitations of an earlier version. In particular the new design reduces wavefront distortions on the pilot mirrors, solves problems with magnification and focus of the fringe localization plane onto the detector, and addresses the variability in sensitivity and resolving power limitations of using a single grating over a large bandpass.