In a subcritical reactor, each neutron produces only neutrons per generation (asymptotically and on average), and thus, the neutron population decreases exponentially in the absence of an external source. The chain reaction is thus easy to stop, making such reactors inherently stable. Interestingly, and contrary to common wisdom, there is no relation between , the external source intensity, and the output power of the reactor. Here, various possible strategies to exploit this fact are presented, and they are applied to the design of a rudimentary multilayer system that allows an arbitrarily large number of fissions per source neutron to be reached, while keeping fixed (here, ). The behavior of the amplifier is verified with simple Monte-Carlo transport simulations. The proposal admittedly brings complications and subtleties that need to be studied further, but, if developed, could allow subcritical reactors to be driven with faint neutron sources, e.g., radioisotope based.