The present case study investigated the potential of the Common European Framework of Reference (CEFR) for languages: learning, teaching, assessment can-do descriptors for mediation in an English for Specific Purposes (ESP) Computer-Assisted Language Learning (CALL)-based context. Fabricating descriptors for mediation was cardinal for the Council of Europe's (2018) endeavour in updating the CEFR Companion. Despite surfacing just as a language skill in the 2001 CEFR Companion, mediation is now viewed as a central mode of communication in the New CEFR Companion, both in the receptive and productive modes. As they were just introduced in 2018, the CEFR mediation descriptor scales have not yet been sufficiently explored. The main goal of the present research was to fill some of this gap in the literature by investigating the potential of the CEFR for languages descriptors for mediation in an ESP CALL-based CEFR B2 tertiary level context (a 13 week ESP course specifically designed to meet the needs of university Rehabilitation Sciences students.) Data collection tools included students' self-assessment against can-do descriptors for mediation, observation, student reflections, and focus group interviews. The findings suggest that the implementation of the existing course activities had the potential to promote mediation processes. The significant role of mediation in carrying out the course activities in addition to the CALL component of the ESP course activities highlighted the potential of CALL technologies to trigger, support, and promote mediation processes; this finding stressed the underlying role of the nature and the structure of the ESP course's CALL-Based activities in supporting mediation processes. [For the complete volume, "Tertiary Education Language Learning: A Collection of Research," see ED614100.]