One of the leading motivations behind the multilingual semantic web is to make resources accessible digitally in an online global multilingual context. Consequently, it is fundamental for knowledge bases to find a way to manage multilingualism and thus be equipped with those procedures for its conceptual modelling. In this context, the goal of this paper is to discuss how common-sense knowledge and cultural knowledge are modelled in a multilingual framework. More particularly, multilingualism and conceptual modelling are dealt with from the perspective of FunGramKB, a lexico-conceptual knowledge base for natural language understanding. This project argues for a clear division between the linguistic and the conceptual dimensions of knowledge. While the conceptual layer is organized into three modules, which result from a strong commitment towards capturing semantic knowledge (Ontology), procedural knowledge (Cognicon) and episodic knowledge (Onomasticon), the linguistic level includes a lexicon and a grammaticon (a syntactic repository of constructional schemata). Cultural mismatches are discussed and formally represented at both the conceptual and the linguistic levels of FunGramKB.