The morphological status of combining-forms (CF) (bio-, -logy, etc.) used in neoclassical compounds (biology, bioscience, etc.) is a matter of debate in morphology. Some see them as having the same status as ordinary words, while others see them as having a special status and forming an independent category. This paper focuses on neoclassical compounds having basic and extended patterns. The former, biology type, is composed solely of CFs, while the latter contains ordinary words, i.e., free morphemes (FM), and is further classified into two categories: bioscience type and hamburgerology type. This paper aims to explain the relationship among those subtypes of neoclassical compounds while capturing their extension processes within the framework of Construction Morphology (CxM). In particular, we outline a novel analysis of those subtypes of neoclassical compounds using “schemas” and “constructional idioms” following the literature regarding CxM.