Purpose: This study introduces a non-orthodox approach to the dominant policy-based approaches to graduate employability through contextualizing international students' everyday experiences within their educational and wider structural contexts of the labour market. Design/methodology/approach: The study used narrative frames to collect data from 180 international students from China, Hong Kong, India, Sri Lanka, Vietnam and Nepal at a New Zealand tertiary institution. Narrative frames as a research tool in educational contexts are used to ellicit the experiences of individuals in the form of a story as participants reflect on their experience. The frames use sentence starters to draw responses from participants about their experiences (Barkhuizen and Wette, 2008). Findings: This study argues that, through a socialization process, international students develop identities that fit an ever-changing labour market. This process is catalysed by a higher education landscape that produces career-ready subjects capable of appropriating different social spaces that prepare students and graduates to enter the labour market. Further, it argues that graduate employability should be understood as a complex process through which students and graduates socialise themselves through negotiating the socioacademic spaces by (1) familiarising themselves with the dominant workspace norms, (2) positioning themselves as more career-ready individuals, and (3) imagigining employable selves capable of meeting the needs of the job market. Research limitations/implications: This study has limitations. Only one data collection source has been used. It would have been great to use narrative frames along with interviews. In addition, the data would have been stronger if the researcher could have used classroom observations, which could be a future initiative. Practical implications: This study could provide practical insights to tertiary institutions about international students' developing capabilities and identities so they could better prepare themselves for the world of work. Further, this study provides insights about some of the challenges that international students face in tertiary contexts to become career-ready. Hence, educators could employ strategies to better support these learners in their everyday learning spaces. This study also has useful benefits for future and current international students and international graduates regarding what investments they need to make so they can better socialize themselves in their tertiary and workplace practices. Social implications: This study has social implications. It helps international students better understand the social, cultural and academic expectations of their host countries. Therefore, they could better socialize themselves into those practices and contribute more effectively to their academic and workplace communities. The study also helps academic and workplace institutions strategize more effectively to address the social and cultural needs of international graduates. The study also contributes to the social and cultural understanding of the teachers that engage with international students on a daily basis by helping them devise activities that better address these students' and graduates' needs. Originality/value: The study adds theoretical and methodological value to the debates around graduate employability. It includes the voices of 180 students and unravels their day-to-day experiences of capability building and employability development from their own perspectives.