5G AgiLe and fLexible integration of SaTellite And cellulaR (5G-ALLSTAR) is a Korea-Europe (KR-EU) collaborative project for developing multi-connectivity (MC) technologies that integrate cellular and satellite networks to provide seamless, reliable, and ubiquitous broadband communication services and improve service continuity for 5G and beyond. The main scope of this project entails the prototype development of a millimeter-wave 5G New Radio (NR)-based cellular system, an investigation of the feasibility of an NR-based satellite system and its integration with cellular systems, and a study of spectrum sharing and interference management techniques for MC. This article reviews recent research activities and presents preliminary results and a plan for the proof of concept (PoC) of three representative use cases (UCs) and one joint KR-EU UC. The feasibility of each UC and superiority of the developed technologies will be validated with key performance indicators using corresponding PoC platforms. The final achievements of the project are expected to eventually contribute to the technical evolution of 5G, which will pave the road for next-generation communications.