Efficient and scalable solution algorithms for systems of linear equations are crucial for monolithic solution schemes in coupled multi-physics systems. These solvers and preconditioners need to address the coupling between fields where the coupling domain is often of lower dimensionality than the problem itself, for example surface coupling in fluid/solid interactions [1, 3] or contact mechanics [4] or line coupling of slender fibers embedded into solid continua [2]. Such couplings present unique challenges due to significant differences in the sizes of the individual subdomains — both the physical fields and the coupling interfaces. These disparities affect not only partitioning strategies in parallel computing but also the design and performance of algebraic multigrid preconditioners, particularly in terms of coarsening strategies. A critical question in this context is whether the off-diagonal coupling blocks should be included in the coarsening process. While some approaches, such as those described in [3, 4], incorporate these blocks, others achieve comparable performance without them [1, 2]. However, the impact of these strategies on scalability has not been systematically explored. This presentation examines the scalability of monolithic solution schemes for coupled multi-physics systems, focusing on algebraic multigrid preconditioners for block matrices. Relevant applications will include surface-coupled fluid/solid interaction or contact problems and line-coupled beam/solid interaction. Computational experiments leverage the open-source multigrid package MueLu from the Trilinos project (https://trilinos.github.io).