U.S. Armed Forces conduct operations in diverse international settings. These forces interact not only with the populations of the host county, but also with cooperating military from other national backgrounds. U.S. Forces are likely to operate in multiple different cultural settings over the course of their careers. Working with a respect of these cultures, as opposed to against them, or in ignorance of them, is conducive to mission success. Fortunately, there has been a recent increase in focus on cultural training within the military. Unfortunately, a majority of the existing training is culture-specific (i.e., focused on one country or region) and can only partially prepare individuals for numerous multicultural interactions. In fact, the specific knowledge learned about one culture can be rendered ineffective or even offensive when applied in another culture. Although culture-specific knowledge is conducive to mission success, effective performance across a variety of cultural settings also requires an emphasis on on-the-spot cultural learning and adaptation. Recent research suggests that cultural success is just as much about general adaptability within ambiguous, complex settings as it is about specific knowledge of a culture. This paper presents a framework distilled from the scientific literature that can be used to build training to develop the culture-general (i.e., not dependent on particular cultures or cultural dimensions) skills of our Armed Forces. The framework draws from the multidisciplinary cultural competence literature to suggest that individuals who possess a set of basic cognitive, behavioral, and motivational characteristics will demonstrate stronger on-the-spot cultural learning. This learning, in turn, will allow individuals to adapt to new cultural situations and make better use of their culture-specific knowledge. In sum, the presented framework suggests that training individuals' self-awareness, social awareness, flexibility, self-management, openness to experience, and multiculturalism will lead to more intercultural success, improving the chances for mission success.