  Multiphase estimation is a paradigmatic example of a multiparameter problem.
When measuring multiple phases embedded in interferometric networks,
specially-tailored input quantum states achieve enhanced sensitivities compared
with both single-parameter and classical estimation schemes. Significant
attention has been devoted to defining the optimal strategies for the scenario
in which all of the phases are evaluated with respect to a common reference
mode, in terms of optimal probe states and optimal measurement operators. As
well, the strategies assume unlimited external resources, which is
experimentally unrealistic. Here, we optimize a generalized scenario that
treats all of the phases on an equal footing and takes into account the
resources provided by external references. We show that the absence of an
external reference mode reduces the number of simultaneously estimatable
parameters, owing to the immeasurability of global phases, and that the
symmetries of the parameters being estimated dictate the symmetries of the
optimal probe states. Finally, we provide insight for constructing optimal
measurements in this generalized scenario. The experimental viability of this
work underlies its immediate practical importance beyond fundamental physics.

Quantum Physics;Optics