When a disaster occurs during a pandemic, it would be a case of concurrent crises (synonymous to cascading disasters or compounding disasters). The single-hazard approach to disaster response system is not suited for this scenario. As shown from the experiences of the Philippines, India, Japan, and the Republic of Korea, the conventional single-hazard approach needed to integrate new measures, including basic skills training on handling COVID-19 for disaster responders; additional stockpiles of face coverings, disinfectants, tents, and personal protective equipment (PPE); social distancing at evacuation centers; updating of standard operation procedures (SOPs) and guidelines for disaster response to adapt to the concurrent crises situations. Building on the reports presented by the member countries of Asian Disaster Reduction Center (ADRC), this paper highlights three evolving disaster response practices during the COVID-19 pandemic: (i) digitalization of some aspects of disaster response, including early warning, surveillance, and impact assessment; (ii) dispersed evacuation to enforce social distancing, including other measures such as testing, tracing, and isolating infected individuals; (iii) remote psychological first aid to disaster-impacted individuals who are already experiencing anxieties from the pandemic. Indicative outcomes of the evolving response practices are discussed, including whether these could serve as entry points to transition the disaster response system from a single-hazard approach towards a multihazard approach.