Abstract <p>We propose the adaptive block algebraic method to solve the multiphysics problems arising from the collocated finite volume discretization methods. The method is specifically designed to solve multiphysics problems featuring various physics in various parts of the domain, resulting in block-structured saddle-point linear algebraic systems with variable block size. The adaptive algebraic multigrid method uses available information on the eigenvectors of the problem to construct prolongation and restriction operators. The information on the distribution of degrees of freedom within the blocks to form an initial set of vectors is used. It was shown that the arising linear systems are amenable to the solution with the proposed method. Various approaches to strong point selection, coarse space refinement, and bootstrapping the test vectors are discussed and analysed. In this work, we address the systems arising from coupled problems of free-flow and poroelasticity, frictional rigid body contact mechanics, and poroplasticity with fractures. All of the problems are of saddle-point nature.</p>