Bounded natural functors (BNFs) provide a modular framework for the construction of (co)datatypes in higher-order logic. Their functorial operations, the mapper and relator, are restricted to a subset of the parameters, namely those where recursion can take place. For certain applications, such as free theorems, data refinement, quotients, and generalised rewriting, it is desirable that these operations do not ignore the other parameters. In this paper, we generalise BNFs such that the mapper and relator act on both covariant and contravariant parameters. Our generalisation, BNF_CC, is closed under functor composition and least and greatest fixpoints. In particular, every (co)datatype is a BNF_CC. We prove that subtypes inherit the BNF_CC structure under conditions that generalise those for the BNF case. We also identify sufficient conditions under which a BNF_CC preserves quotients. Our development is formalised abstractly in Isabelle/HOL in such a way that it integrates seamlessly with the existing parametricity infrastructure.