Research software is an essential output in different research domains and needs to be reproducible and extendable throughout future research. Achieving this requires shared principles and know-how among researchers and research institutes. The European Software Sustainability Infrastructure (EuSSI) consortium aims towards identifying key elements and providing common grounds to achieve such a goal in European level. Partners in the EuSSI consortium are all involved - in one way or another - in research software and share a common interest in improving the general quality of research software. This document outlines the EuSSI consortium vision for supporting research software sustainability.