  Radio relics could be generated by multiple shocks induced in the turbulent
intracluster medium during galaxy mergers. Kang (2021) demonstrated that the
re-acceleration of cosmic ray (CR) protons via diffusive shock acceleration
(DSA) by multiple shocks could enhance the acceleration efficiency and flatten
the CR spectrum, compared to a single episode of DSA. Here we examine the CR
electron acceleration through multiple re-acceleration by considering energy
losses and decompression of the particle distribution and magnetic fields in
the postshock region between consecutive shock passages. We find that the
accumulated effects of repeated re-acceleration are significant, if preceding
shocks are stronger than the last shock and the shock passage interval is
$\lesssim20$ Myr. In such cases, both the CR spectrum and the ensuing radiation
spectrum behind the last shock are enhanced and become flatter than the
canonical DSA power-law forms. As a result, the shock Mach number estimated
from radio observations tends be higher than the actual Mach number of the last
shock. Thus, multiple episodes of DSA may explain the enhanced acceleration
efficiency for CR electrons and the discrepancy of shock Mach numbers, $M_{\rm
X} \lesssim M_{\rm rad}$, inferred for some observed radio relics.
