This paper presents a new mereological approach to formalizing geometric notions of incidence, congruence, and parallelism over extended regions. The axiomatization was built extending a decidable pre-mereological base language, showing where the geometric framework requires first-order extension. Important outcomes are in the investigation of how to define incidence between extended geometric objects that are suitable candidates to replace points, lines, and planes in a purely region-based first-order framework. Moreover, the mereogeometric approach proposed is shown to have a key advantage in allowing dimensionality to be a relative concept in contrast to it being an absolute concept encoded in the types of geometric entities. Especially this property, one may conclude, could make mereogeometry attractive for formalizing geometric relations in a cognitively adequate manner for applications that require the same flexibility of switching between conceptualizations of space of different dimensionality as human beings show in language use.