  We consider the optimal site selection of future generations of gravitational
wave detectors. Previously, Raffai et al. optimized a 2-detector network with a
combined figure of merit. This optimization was extended to networks with more
than two detectors in a limited way by first fixing the parameters of all other
component detectors. In this work we now present a more general optimization
that allows the locations of all detectors to be simultaneously chosen. We
follow the definition of Raffai et al. on the metric that defines the
suitability of a certain detector network. Given the locations of the component
detectors in the network, we compute a measure of the network's ability to
distinguish the polarization, constrain the sky localization and reconstruct
the parameters of a gravitational wave source. We further define the
`flexibility index' for a possible site location, by counting the number of
multi-detector networks with a sufficiently high Figure of Merit that include
that site location. We confirm the conclusion of Raffai et al., that in terms
of flexibility index as defined in this work, Australia hosts the best
candidate site to build a future generation gravitational wave detector. This
conclusion is valid for either a 3-detector network or a 5-detector network.
For a 3-detector network site locations in Northern Europe display a comparable
flexibility index to sites in Australia. However for a 5-detector network,
Australia is found to be a clearly better candidate than any other location.
