  We demonstrate to what extent many copies of maximally entangled two-qubit
states enable for generating a greater amount of certified randomness than that
can be certified from a single copy. Although it appears that greater the
dimension of the system implies a higher amount of randomness, the
non-triviality lies in the device-independent simultaneous certification of
generated randomness from many copies of entangled states. This is because,
most of the two-outcome Bell inequalities (viz., Clauser-Horne-Shimony-Holt,
Elegant, or Chain Bell inequality) are optimized for a single copy of two-qubit
entangled state. Thus, such Bell inequalities can certify neither many copies
of entangled states nor a higher amount of randomness. In this work, we
suitably invoke a family of $n$-settings Bell inequalities which is optimized
for $\lfloor n/2 \rfloor$ copies of maximally entangled two-qubit states,
thereby, possess the ability to certify more randomness from many copies of
two-qubit entangled state.
