Understanding the physics of 4d confining gauge theories is one of the biggest open problems in QFT. In general, this problem is hard to solve as our usual analysis tools break down in real world examples of confinement. However, there is a collection of models, called center-stabilized compactifications, which are engineered to be confining while allowing perturbative and semiclassical analysis, providing insight into how confinement can come about in general. Several examples of center-stabilized compactifications have been found and understood, but they have all been considered separately from each other. In this talk, I will present my work on building connections between these different models with the goal of understanding the entire landscape of confining gauge theories.