  In this work, we investigate the problem of multiphase estimation using
generalized $3$- and $4$-mode Mach-Zehnder interferometer. In our setup, we
assume that the number of unknown phases is the same as the number of modes in
the interferometer, which introduces strong correlations between estimators of
the phases. We show that despite these correlations and despite the lack of
optimisation of a measurement strategy (a fixed interferometer is used) we can
still obtain the Heisenberg-like scaling of precision of estimation of all the
parameters. Our estimation scheme can be applied to the task of
quantum-enhanced sensing in 3-dimensional interferometric configurations.
