Frontline workers (FLWs) provide essential services necessary for a functioning society, but the nature of their work contributes to their high rates of burnout. This burnout impacts not only their own health, but also has dire consequences for the people most in need of their services. Digital interventions for burnout may provide scalable, accessible, and cost-effective care. However, such interventions have been designed to intervene at the individual-level and have been inadequate in sustainably alleviating burnout. In addition, these interventions have not considered how we might integrate more effective organizational-level strategies or reflect FLWs' own experiences and the unique contexts of frontline work in their design. One important, yet understudied, domain of frontline work that experiences high rates of burnout is gender-based violence (GBV) service provision in nonprofit organizations. Using a community-based participatory research approach, we ran 8 co-design workshops with FLWs and supervisors from various nonprofit GBV organizations in a large metropolitan city in the United States to understand their experiences, hopes, and perceptions of technology for burnout support within their organizations. We found that participants greatly valued their support systems and supervisory relationships at work. And while there was a desire to use technology as support tools for burnout, participants were wary of how it could conflict with these support systems and important organizational values. We contribute a multilevel framework for digital burnout interventions and argue for a methodological shift to an assets-based approach, reframing the future of research and design of burnout interventions to center and reflect the needs, values, and lived experiences of FLWs.