Feature models originating from Software Product Line Engineering are a well-known approach to variability modeling. In many situations, the variability does not apply only on features but also on the number of times these features can be cloned. In such a case, cardinality-based feature models are used to specify the number of clones for a given feature. Although previous works already investigated approaches for feature modeling with cardinality, there is still a lack of support for constraints in the presence of clones. To overcome this limitation, we present an abstract model to define constraints in cardinality-based feature models and propose a formal semantics for this kind of constraints. We illustrate the practical usage of our approach with examples from our recent experiences on cloud computing platform configuration.