BK-based matching exploits external background knowledge resources (BK) to fill the semantic gap between the ontologies to align. Existing BK-based matchers implement the indirect matching approach in their internal architecture, which makes any adaptation or reuse of the code difficult. Indeed, to improve a particular step in the BK-based matching process, it is necessary to code the whole process from scratch which requires a lot of time and effort. To overcome this issue, we propose a flexible framework called Generic BK-based Matcher (GBKOM). GBKOM is an extension that can be added to any existing matcher. It is a configurable framework that implements the BK-based matching process, with a rich set of parameters making it customizable and suitable for performing experimental evaluations. GBKOM has participated, with YAM++ as a direct matcher, in the OAEI 2017 and OAEI 2017.5 campaigns, where it has been successful on the biomedical benchmarks, and top ranked in several tasks. Furthermore, we have performed experiments with two other direct matchers (i.e., LogMap and LogMapLite) to show that the effectiveness of GBKOM is independent of the direct matcher used.