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.