  Network Bell experiments give rise to a form of quantum nonlocality that
conceptually goes beyond Bell's theorem. We investigate here the simplest
network, known as the bilocality scenario. We depart from the typical use of
the Bell State Measurement in the network central node and instead introduce a
family of symmetric iso-entangled measurement bases that generalise the
so-called Elegant Joint Measurement. This leads us to report noise-tolerant
quantum correlations that elude bilocal variable models. Inspired by these
quantum correlations, we introduce network Bell inequalities for the bilocality
scenario and show that they admit noise-tolerant quantum violations. In
contrast to many previous studies of network Bell inequalities, neither our
inequalities nor their quantum violations are based on standard Bell
inequalities and standard quantum nonlocality. Moreover, we pave the way for an
experimental realisation by presenting a simple two-qubit quantum circuit for
the implementation of the Elegant Joint Measurement and our generalisation.
