Max-stable distribution functions are theoretically grounded models for modelling multivariate extreme values. However they suffer from some striking limitations when applied to real data analysis due to the intractability of the likelihood when the number of variables becomes high. Cumulative Distribution Networks (CDN's) have been introduced recently in the machine learning community and allow the construction of max-stable distribution functions for which the density can be computed. Unfortunately, we show in this work that the dependence structure expected in the data may not be accurately reflected by max-stable CDN's. To face this limitation, we therefore propose to augment max-stable CDN's with the more standard Gumbel max-stable distribution function in order to enrich the dependence structure.