Globalized English offers interaction platforms, including cyber-based settings, for linguistically and culturally diverse speakers, particularly in the English as a second language/English as a foreign language context. Thus, it requires developing the intercultural competence of the parties involved. English users' different perspectives may challenge effective communication and interaction. This paper results from a collaboration project between an Omani higher learning institution and an American higher learning institution and reports an exploratory study that examined the understanding and use of intercultural communicative competencies by 15 undergraduate users of English. Data was collected from the sample participants' notes on material analysis, collaborative projects, test performances, and the instructors' field observations. Data analysis examined the participants' intercultural intelligence in various communicative settings in English. The findings showed the participants changed certain predetermined misconceptions about the "other culture" and developed positivity and acceptance of intercultural differences. Results also highlighted the significance of online academic internationalization and incorporating intercultural competence in the English as a second language/English as a foreign language curricula. The study further indicated the significance of the teacher's role in nurturing learners' intercultural competence and intercultural-awareness priorities for being the global citizens of today.