Fiber-optic Mach-Zehnder interferometers are widely used in research areas such as telecommunications, spectroscopy, and quantum information. These optical structures are known to be affected by phase fluctuations that are usually modeled as multiparametric noise. This multidimensional noise must be stabilized or compensated for to enable fiber-optic Mach-Zehnder architectures for practical applications. In this work, we study the effectiveness of a modified Perturb-and-Observe (P&O) algorithm to control multidimensional phase noise in fiber-based multi-arm Mach-Zehnder interferometers. We demonstrate the feasibility of stabilizing multidimensional phase noise by numerical simulations using a simple feedback control scheme and analyze the algorithm's performance for systems up to dimension 8x8. We achieved minimal steady-state errors that guarantee high optical visibility in complex optical systems with NxN matrices (with N=[2,3,4,5,6,7,8]).