Quantum correlations are an essential resource in advanced information processing based on quantum phenomena. Remarkably, the vacuum state of a quantum field may act as a key element for generation of strong quantum correlations. Besides, superconducting microwave cavities offer an excellent platform for experimental studies of such quantum effects. In this work, we numerically investigate vacuum correlations in a flux-tunable superconducting cavity under multiple pump tones. We consider double and triple pumping cases and explore pairwise correlations between three frequency bands specified within a single cavity resonance. Our work shows that three pumps produce more correlations than two pumps; thus, quantum resources facilitated by the triple pump scheme offers enhanced prospects for quantum data processing using parametric microwave cavities.