Phoenix aims to develop a fundamentally novel computational model for reconstructing complex software systems, following some massive internal failure or external infrastructure damage. Recovering system operations is a challenging problem as it may require excessive system reconstruction using a different infrastructure (i.e., computational and communication devices named system cells) from the one that the system was originally designed for. Thus, software functionality may have to be remodularised and allocated onto devices with very different characteristics than the ones originally used but with some generic capabilities. Phoenix aims to develop a bio-inspired paradigm for reconstructing nearly extinct complex software systems based on a novel computational DNA (co-DNA) oriented systems modelling approach. The co-DNA will encapsulate logic and program code and will enable the use of analogues of biological processes for transmitting, transforming, combining, activating and deactivating it across computational and communication devices. The purpose of encoding the co-DNA of a system, and computational analogues of biological processes using it, is to enable other computational devices receiving the co-DNA to act as parts of the system that needs to be reconstructed, realise chunks of its functionality, and spread further the system reconstruction process. The Phoenix approach will bring a breakthrough in the current software system design and engineering paradigm. This will be through, not only a fundamentally new way of engineering mechanisms to support the resilience, continuity and recovery of software systems, but also the initiation of a new paradigm of designing and implementing software systems, based on the encoding of a system co-DNA that can trigger processes of self-regulated and incrementally expanding system functionality.