This work assesses the feasibility of using a small, safe, and inexpensive keff 0.98 subcritical fission assembly [subcritical neutron multiplier (SCM)] to amplify the treatment neutron beam intensity attainable from a compact deuterium-deuterium (D-D) fusion neutron source delivering [approximately]1012 n/s. The objective is to reduce the treatment time for deep-seated brain tumors to [approximately]1 h. The paper describes the optimal SCM design and two optimal beam-shaping assemblies (BSAs) - one designed to maximize the dose rate and the other designed to maximize the total dose that can be delivered to a deep-seated tumor. The neutron beam intensity amplification achieved with the optimized SCM and BSA results in an increase in the treatment dose rate by a factor of 18: from 0.56 Gy/h without the SCM to 10.1 Gy/h. The entire SCM is encased in an aluminum structure. The total amount of 20% enriched uranium required for the SCM is 8.5 kg, and the cost (not including fabrication) is estimated to be less than $60,000. The SCM power level is estimated at 400 W when driven by a 1012 n/s D-D neutron source. This translates into consumption of only [approximately]0.6% of the initially loaded 235U atoms during 50 years of continuous operation and implies that the SCM could operate continuously for the entire lifetime of the facility without refueling. Cooling the SCM does not pose a challenge; it may be accomplished by natural circulation as the maximum heat flux is only 0.034 W/cm2.