We study quasi-one-dimensional strongly correlated materials using a multi-step approach based on density functional theory, downfolding techniques, and tensor-network simulations. The downfolding procedure yields effective multiband Hubbard models that capture the competition between electron hopping and local Coulomb interactions relevant to the system’s low-energy properties. The resulting multiband Hubbard models are solved using matrix product states. Applied to (_2_3), (_2_3), (_3), and (_2_3), this purely one-dimensional treatment yields very small long-range magnetic order, in contrast to the magnetic ordering observed experimentally. To account for this behavior, we extend the multi-step approach by incorporating interchain couplings through a self-consistent mean-field scheme. This combined approach stabilizes larger finite staggered magnetizations, providing a consistent description of magnetic order in agreement with experiment. For (2{3.5}) and (_2), we also tested an approach proposed for ladder materials, however, we find that these materials are not well suited for this approach due to the small magnitude of the intraladder hopping parameters.