Sustainability is an emerging topic in the field of requirements engineering. In general, five sustainability dimensions can be distinguished: economical, environmental, technical, social and individual. Software requirements can have positive and negative impacts on these different dimensions. A number of methods and frameworks have been already proposed that deal with the question on how impacts of software requirements on sustainability can be identified and managed as part of requirements engineering. Some open questions, however, remain: How can sustainability be supported by using agile development practices from frameworks like Scrum? Is it productive to consider sustainability in sprint planning meetings or product reviews? Is it useful to add sustainability aspects to acceptance criteria of user stories or a definition of done? This paper describes an ongoing doctoral study that attempts to find answers on the prior questions. The goal is to develop a sustainability-aware Scrum framework inspired by existing requirements engineering methods to improve the sustainability impacts of software systems and to make software as sustainable as possible.