Consider two different portfolios which have claims triggered by the same events. Their corresponding collective model over a fixed time period is given in terms of individual claim sizes and a claim counting random variable N. In this paper, we are concerned with the joint distribution function (df) F of the largest claim sizes . By allowing N to depend on some parameter, say , then is for various choices of N a tractable parametric family of bivariate dfs. We investigate both distributional and extremal properties of . Furthermore, we present several applications of the implied parametric models to some data from the literature and a new data-set from a Swiss insurance company (Data-set can be downloaded here http://dx.doi.org/10.13140/RG.2.1.3082.9203.)