This dissertation sets out to find an answer to the question why not all logically conceivable patterns are found typologically. In other words, my aim is to find paradigmatic gaps and explain their absence. In doing so, I use the mathematical notion of monotonicity (which is a more general term to convey order preservation) as proposed by Graf (2019a) to probe the upper bound on the range of typological variation within morphosyntax. Specifically, I focus on (im)possible patterns in verb stem syncretism, resolved gender agreement, and person-number syncretism. Each morphosyntactic domain comes with a base hierarchy, and the mapping from this hierarchy to surface forms must be order-preserving. Patterns of syncretism in verbal paradigms are problematic for the more restrictive *ABA generalization of Bobaljik (2012), based on which two forms cannot be identical to the exclusion of any forms between them. But with a hierarchy that is independently motivated by Reichenbach's tense system (1947), they all follow monotonicity. Resolved gender agreement occurs with coordination structures, where combinations of two distinct genders are resolved into a different gender value. The gender hierarchy used for gender resolution rules is directly extracted from the organization of the cross-linguistic data to capture all the possible resolution patterns and ban the unattested ones. The intrinsically 2-dimensional hierarchy of person-number emerges when we combine language-specific and cross-linguistic analyses of patterns of person-number syncretism. Languages can choose from a set of six logical hierarchies. In each language, then, only those patterns are allowed that guarantee monotonic mappings over the base hierarchy. The findings reported in this research lend further empirical support to the idea that monotonicity is a linguistic universal that extends beyond semantics. The major advantage of the presented account is that it combines substantive universals (linguistic hierarchies) and formal universals (monotonicity) to give a tighter characterization of morphosyntactic phenomena. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]