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Generalising the uniform companion for large fields with a single derivation,we construct a theory $\text{UC}_{\mathcal{D}}$ of fields of characteristic $0$with free operators -- operators determined by a homomorphism from the field toits tensor product with $\mathcal{D}$, a finite-dimensional$\mathbb{Q}$-algebra -- which is the model companion of any theory of a fieldwith free operators whose associated difference field is difference large andmodel complete. Under the assumption that $\mathcal{D}$ is a local ring, weshow that simplicity is transferred from the theory of the underlying field tothe theory of the field with operators, and we use this to study the modeltheory of bounded, PAC fields with free operators.

The uniform companion for fields with free operators in characteristic zero