Multi-story buildings are an alternative for any developing city facing population growth and land scarcity. Recently, verticalization of the built environment has considered the possible use of confined masonry (CM) buildings because they combine adequate strength, lower construction and maintenance costs, and durability. This has brought attention to the possibility of extending the current knowledge for the design of low-rise CM buildings to mid-rise buildings. This paper discusses the conceptual design challenges from the fact that CM walls are designed to develop shear damage, which leads to the formation of an undesirable damage mechanism that reduces the global deformation capacity of the buildings as their height increases. To provide quantitative context, four models of 8 and 10-story buildings designed according to the Mexico City Building Code, and having walls built with high-strength masonry and horizontal joint reinforcement, were analyzed. The wide-column model and an idealized backbone curve, calibrated with experimental data, were used, respectively, to model the buildings and the nonlinear behavior of the walls. From the global properties and performance of the buildings, it is concluded that the current design approach for CM walls leads to the formation of a soft story, and an excessive damage concentration that compromises the global stability of mid-rise CM buildings for displacement demands smaller than those assumed during the design.