In this work, we combine probabilistic constellation shaping (PCS) using a Maxwell Boltzmann distribution with multi-dimensional modulations with the purpose of increasing performance gains in both the linear and non-linear regimes of optical fiber transmission systems. We particularly study the case of polarization division multiplexed long-haul coherent systems. By applying set partitioning and energy constraints on four-dimensional (4D) modulations followed by probabilistic shaping, we give insights into constructing novel modulations with enhanced performance compared to conventional PCS constellations in which shaping is performed separately over each real dimension.