Biological entities are key elements of biomedical research. Their definition and their relationships are important in areas such as phylogenetic reconstruction, developmental processes or tumor evolution. Hypotheses about relationships like phenotype order are often postulated based on prior knowledge or belief. Evidence on a molecular level is typically unknown and whether total orders are reflected in the molecular measurements is unclear or not assessed. In this work we propose a method that allows a fast and exhaustive screening for total orders in large datasets. We utilise ordinal classifier cascades to identify discriminable molecular representations of the phenotypes. These classifiers are constrained by an order hypothesis and are highly sensitive to incorrect assumptions. Two new error bounds, which are introduced and theoretically proven, lead to a substantial speed-up and allow the application to large collections of many phenotypes. In our experiments we show that by exhaustively evaluating all possible candidate orders, we are able to identify phenotype orders that best coincide with the high-dimensional molecular profiles.