Above 20 MeV the standard spheres of a Bonner sphere spectrometer (BSS) have similar responses, both in shape and sensitivity. The responses of the standard set also exhibit strongly diminishing sensitivities above 20 MeV. In the current work the Monte Carlo N-Particle eXtended (MCNPX) code was used to investigate different design modifications to increase the high-energy neutron response of a BSS. The cost-effective system expands upon the design of an existing, commercially available BSS system by adding concentric shells of copper, tungsten, and lead. These shells are used in various combinations with the existing spheres. The design, referred to as the Bonner sphere extension (BSE), incorporates both passive and active detection techniques including activation foils and the standard 6LiI(Eu) scintillator. Detailed models in MCNPX were used to create fine-group neutron responses from thermal to 1000 MeV. Measurements were performed with the BSE at Los Alamos Neutron Science Center, and the data were unfolded using the MXD-FC33 code and the calculated BSE response matrix. The resulting spectrum demonstrated the BSE system provided improvement in the measurement of the neutron spectra in the energy regions above 20 MeV when compared to the standard Bonner sphere system. The BSE system extends the sensitivity of the system to more than ten decades in energy while maintaining a nearly isotropic angular response.