In its most common form, extreme value theory is concerned with the limiting distribution of location-scale transformed block-maxima of a sequence of identically distributed random variables. In case the members of the sequence are independent, the weak limiting behavior of the maximum is adequately described by the classical Fisher--Tippett--Gnedenko theorem. In this presentation we are interested in the case of dependent random variables, while retaining a common marginal distribution function for all members of the sequence. This approach is facilitated by highlighting the connection between block-maxima and copula diagonals in an asymptotic context. The main goal of this presentation is to discuss a generalization of the Fisher--Tippett--Gnedenko theorem in this setting, leading to limiting distributions that are not in the class of generalized extreme value distributions.