Discourse relations are an important means to achieve coherence, and they form the basis for existing mainstream discourse frameworks, such as RST, PDTB, and SDRT. These frameworks differ in assumptions about discourse relations and structural constraints of discourse organization. The relationship between these frameworks has been an open research question. The UniDim approach proposed by Sanders et al. (Corpus Linguistics and Linguistic Theory, 17(1):1–71, 2021) provides a way of decomposing discourse relations into cognitively inspired dimensions, which serve as an interlingua for representing discourse relations across different frameworks. This study explores how the UniDim proposal can be applied to discourse relation classification across different frameworks. Our experimental results on RST, PDTB, and SDRT from the DISRPT benchmark (Braud et al., DISRPT: A multilingual, multi-domain, cross-framework benchmark for discourse processing, 2024) indicate that the upper limits attainable with the UniDim proposal are quite high across different frameworks, while using predicted UniDim dimensions for discourse relation classification causes large performance drops. It is found that classes with a small amount of training data are responsible for the overall significant performance drops. Meanwhile, under-specified classes of UniDim dimensions are challenging for automatic methods, calling for further studies on the mapping rules between discourse relations and the dimensions of the UniDim proposal.