From the perspective of intersubjectivity, this study examines English general extenders in interpersonal interaction and their implications for cross-cultural communication. Based on spoken language corpora from existing literature and by integrating politeness strategy theory with the Gricean Cooperative Principle, the research findings reveal that general extenders exert pragmatic functions guided by politeness strategies, which are rooted in intersubjectivity and closely related to the addressee's self-image, covering both positive and negative politeness. Specifically, conjunctive extenders enhance social closeness through shared experiences (positive politeness) and perform a hedging function regarding informativeness in line with the Quantity Maxim; disjunctive ones mitigate tone via alternative possibilities (negative politeness) and maintain caution about information accuracy based on the Quality Maxim. Their intersubjective function relies on the subjectively assumed shared knowledge, experiences and conceptual frameworks between communicators, enabling information omission and listener inference. Mastery of these extenders facilitates smooth cross-cultural communication by negotiating shared knowledge, and the research findings provide solid theoretical and practical support for cultivating socio-pragmatic competence in EFL teaching.