We present a conceptual design for a high-resolution optical spectrograph appropriate for mounting at Cassegrain on a large aperture telescope. The design is based on our work for the Gemini High Resolution Optical Spectrograph (CUGHOS) project. Our design places the spectrograph at Cassegrain focus to maximize throughput and blue wavelength coverage, delivering R=40,000 resolving power over a continuous 320-1050 nm waveband with throughputs twice those of current instruments. The optical design uses a two-arm, cross-dispersed echelle format with each arm optimized to maximize efficiency. A fixed image slicer is used to minimize optics sizes. The principal challenge for the instrument design is to minimize flexure and degradation of the optical image. To ensure image stability, our opto-mechanical design combines a cost-effective, passively stable bench employing a honeycomb aluminum structure with active flexure control. The active flexure compensation consists of hexapod mounts for each focal plane with full 6-axis range of motion capability to correct for focus and beam displacement. We verified instrument performance using an integrated model that couples the optical and mechanical design to image performance. The full end-to-end modeling of the system under gravitational, thermal, and vibrational perturbations shows that deflections of the optical beam at the focal plane are <29 μm per exposure under the worst case scenario (<10 μm for most orientations), with final correction to 5 μm or better using open-loop active control to meet the stability requirement. The design elements and high fidelity modeling process are generally applicable to instruments requiring high stability under a varying gravity vector.