It is widely accepted that necessity comes in different varieties, often called ‘kinds': metaphysical necessity, logical necessity, natural necessity, conceptual necessity, moral necessity, to name but a few – and the same goes for the varieties of possibility. What is usually not fully appreciated, however, is that modal variety is not simply ‘unidimensional': it does not only involve one main variable – kind, whose values are the particular kinds of necessity. Rather, I argue, it is ‘bidimensional', involving two distinct variables – domain and strength. In the first part of the paper, I introduce and develop the proposed bidimensional picture of modal variety, defending it against the common, unidimensional one. In the second part, I consider how the main available accounts of necessities and their relations rely, at least to a significant extent, on the latter picture, pointing out important limitations that they face as a result. I also show how, accordingly, alternative accounts based on a clear and systematic distinction between domain and strength would overcome those limitations. I conclude that, beyond the particular bidimensionalist view defended, our understanding of the modal realm may benefit from more direct debate on whether and how it is multidimensional.