  We study the optomechanical behaviour of a driven Fabry-P\'erot cavity
containing two vibrating dielectric membranes. We characterize the cavity-mode
frequency shift as a function of the two-membrane positions, and report a $\sim
2.47$ gain in the optomechanical coupling strength of the membrane relative
motion with respect to the single membrane case. This is achieved when the two
membranes are properly positioned to form an inner cavity which is resonant
with the driving field. We also show that this two-membrane system has the
capability to tune the single-photon optomechanical coupling on demand, and
represents a promising platform for implementing cavity optomechanics with
distinct oscillators. Such a configuration has the potential to enable cavity
optomechanics in the strong single-photon coupling regime, and to study
synchronization in optically linked mechanical resonators.
