This paper introduces an innovative method for constructing copula models capable of describing arbitrary non-monotone dependence structures. The proposed method enables the creation of such copulas in parametric form, thus allowing the resulting models to adapt to diverse and intricate real-world data patterns. We apply this novel methodology to analyze the relationship between returns and trading volumes in financial markets, a domain where the existence of non-monotone dependencies is well-documented in the existing literature. Our approach exhibits superior adaptability compared to other models which have previously been proposed in the literature, enabling a deeper understanding of the dependence structure among the considered variables.