This study suggests the rethinking of discourse competence in multicultural perspectives and adopts rhetorical, cross-cultural, and critical English for academic purposes (EAP) approaches to argue the three-dimensional structure of such competence, which may increase the intercultural awareness of non-native English learners. According to the Common European Framework of Reference for Languages (CEFRL), discourse competence is a high-level ability that assumes straightforward and efficient communication in English as a lingua franca. The description of discourse competence in the CEFRL adopts a universalistic and text-oriented approach, inherited from the practices of EAP, which disregards discursive practices related to the cultural and social contexts of communication. Excluding social context, discourse competence is structured according to the formal levels of language, and the lexical, grammatical, and generic conventions, without paying sufficient attention to the processes of discourse production and reception. Excluding cultural context, discourse competence is described as a component of communicative competence along with sociocultural competence, focused on the learner's cultural experience. As a result, discourse competence is structured in didactic materials and then developed in teaching practice, without considering the impact of cross-cultural interference between discursive practices involved in the learner's local culture and discourse norms accepted in EAP. A rhetorical approach can overcome the text-oriented approach, which is used in structuring discourse competence. Based on this approach, discourse competence is described at the compositional, argumentative, and emotive levels. The rhetorical approach assumes that text production and text reception should be examined as discursive practices that are socially and culturally constructed and should be analyzed at each level. The three-dimensional structure of discourse competence gives learners an efficient instrument for the gradual analysis of the text at each level, while the text-oriented approach pays most of its attention solely to the organization of the text at the compositional level. A rhetorical approach is suitable to move beyond a universalistic understanding of the text to an intercultural awareness in discursive practices that should be developed through a culturological approach. A cross-cultural approach, usually implemented in business communication, may be applied in academic practice to analyze different socio-cultural contexts of both text production and text reception. The comparative analysis of cultural dimensions allows us to conclude that culturally determined discursive patterns are pertinent mostly at an argumentative level, whereas, it is completely disregarded in the text-oriented structure of discourse competence. A framework of culturally determined discursive patterns, valid for analyzing discourse production and discourse reception at the compositional, argumentative, and emotive levels is suggested. This study points out that the three-level description of discourse competence, focused on cultural dimensions, raises the intercultural awareness of non-native English learners. This study also argues that while discursive patterns are explicitly denoted at the compositional, argumentative, and emotive levels, learners have an analytical framework for comparing discursive patterns grounded in the sociocultural context of discourse production to those of discourse reception. This explicit comparison provides the learners with an opportunity to avoid the negative interference of discursive patterns in text production. Applying a critical EAP approach, this study analyzes how a suggested framework of cultural discursive patterns may be implemented in English, Arab, and Russian academic contexts. Discursive patterns used by researchers are compared with discourse norms adopted in EAP. This study concludes that while the discourse patterns required in EAP remain untouched, a suggested framework provides non-native English writers with a means to avoid the negative interference of discursive patterns, which could disrupt their performance in observing EAP norms.