  In this work we investigate the problem of simultaneous estimation of phases
using generalised three- and four-mode Mach-Zehnder interferometer. In our
setup, we assume that the phases are placed in each of the modes in the
interferometer, which introduces correlations between estimators of the phases.
These correlations prevent simultaneous estimation of all these phases, however
we show that we can still obtain the Heisenberg-like scaling of precision of
joint estimation of any subset of $d-1$ phases, $d$ being the number of modes,
within completely fixed experimental setup, namely with the same initial state
and set of measurements. Our estimation scheme can be applied to the task of
quantum-enhanced sensing in three-dimensional interferometric configurations.
