Time-dependent density functional theory (TDDFT) simulations are conducted on a series of chiral gold/silver alloy nanowires to explore whether silver doping can produce an enhancement of circular dichroism at the plasmon resonance in these systems, and to identify the quantum-mechanical origin of the observed effects. We find a strong plasmonic dichroism when one or two helixes of gold atoms are substituted by silver in a linear chiral nanotube, whose pure gold counterpart does not display any plasmonic dichroism, and we rationalize this finding in terms of "decoupling" the destructive interference of excitations in the pure gold nanotube via alloying. However, further attempts to increase the plasmonic dichroism by considering multi-shell gold nanowires in which one entire shell is doped with silver did not produce the desired effect, but rather a decrease in circular dichroism. We show that this latter result is due to a more severe destructive interference in the dipole excitation contributions, and suggest that further amplification should be possible in principle by properly tuning simultaneously the nanowire structure and chemical ordering.