"""The strong interaction at neutron-rich extremes"" (STRONGINT) will investigate the structure of matter at the neutron-rich frontier in the laboratory and in the cosmos based on chiral effective field theory (EFT) interactions. Chiral EFT opens up a systematic path to investigate many-body forces and provides unique constraints for three-neutron and four-neutron interactions. We will for the first time explore the predicted many-body forces in neutron matter and neutron-rich matter. One milestone will be set by the development of a systematic power counting for neutron-rich matter. This will enable us to carry out diagrammatic approaches, and to develop ground-breaking nonperturbative Monte-Carlo calculations. Our results will strongly constrain the nuclear equation of state at the extremes reached in core-collapse supernovae and neutron stars. Based on the developments for neutron-rich matter, we will investigate spin correlations and develop a systematic description of neutrino-matter interactions, which can set the new standard for supernova simulations. Our pioneering studies have revealed new facets of three-body forces in neutron-rich nuclei, such as their role in determining the location of the neutron dripline in oxygen and in elucidating the doubly-magic nature of calcium-48. We will investigate the impact of chiral three-nucleon forces on key regions in the r-process path and develop a chiral EFT for valence-shell interactions. This will open new horizons for understanding the shell structure of nuclei. Another milestone will be set by the first calculation of neutrino-less double-beta decay based on chiral EFT interactions and consistent electroweak currents. The proposed interdisciplinary problems are essential for a successful and quantitative understanding of these big science questions."