The Large Hadron Collider (LHC) at CERN has been instrumental in recent advances in experimental high energy physics by colliding beams of protons and heavier nuclei at unprecedented energies. The present heavy-ion programme is based mainly on colliding lead nuclei. For future ion runs, there is strong interest to achieve a significantly higher integrated nucleon–nucleon luminosity, which might be achieved through collisions of species other than Pb. In this paper, we explore the intensity and nucleon–nucleon luminosity projections in the LHC for a selection of ion species ranging from He to Xe, and including Pb as reference. Alternative beam production schemes are investigated as a way to mitigate effects such as space charge that degrade the beam quality in the LHC injectors. In the most optimistic scenarios, we find up to about a factor 4 improvement in integrated nucleon–nucleon luminosity for a typical future one-month run, with respect to the present Pb programme. We also outline a future study programme and experiments to test the assumptions and refine the simulated projections put forward in this article.