Background: Research shows that emotional intelligence (EI) should be used alongside cognitive intelligence during requirements change (RC) handling in Software Engineering (SE), especially in agile settings. Objective: We wanted to study the role of EI in-depth during RC handling. Method: We conducted a mixed-methods study (an interview study followed by a survey study) with 124 software practitioners. Findings: We found the causal condition, intervening condition and causes lead to key direct consequences of regulating own emotions, managing relationships, and extended consequences of sustaining productivity, setting and sustaining team goals. We found several strategies for supporting EI during RC handling. Further, we found strong correlations between six strategies and one being aware of own emotions, regulating own emotions, sustaining team productivity, and setting and sustaining team goals. Conclusion: Empathising with others and tracking commitments and decisions as a team are key strategies that have strong correlations between managing emotions, between sustaining team productivity, and between setting and sustaining team goals. To the best of our knowledge, the framework we present in this paper is the first theoretical framework on EI in SE research. We provide recommendations for software practitioners to consider during RC handling. Summary of Implications: An immediate implication of the work is a problem-solution guide (given in the paper) that comprises strategies which can be deployed in various scenarios, including emotional awareness and regulation at individual level, and productivity sustainment and goal set and sustainment at team level. Further Work: Informed by the findings of this paper, we later developed a GPT-4 integrated developer insights platform where the development team’s responses to RCs generate summaries and recommendations for engineering managers to better guide the team.