Ample groupoids that are neither almost finite nor purely infinite

We investigate a question posed by Matui concerning the existence of minimal ample groupoids that are neither almost finite nor purely infinite, along with several natural variations of this problem. We begin by noting that there exists minimal, effective, ample transformation groupoids with this property. Moreover, such examples can be chosen to be either principal or amenable. We then construct new examples of essentially principal ample groupoids that are likewise neither almost finite nor purely infinite. These examples rely on the recent twisted topological groupoid construction of Palmer and Wu. In particular, our examples do not arise from transformation groupoids.