Ionic liquids are versatile compounds for biotechnological applications. However, even the chemical systems composed only of the IL, water, and of the biomolecules display complex interactions that are not reducible in terms of the possible pairs of components. Here, we illustrate this complexity and provide a molecular understanding of cooperative solvation effects by studying Ubiquitin in solutions of the four ionic liquids formed by the combinations of the cations 1-Ethyl-3-methylimidazolium (EMIM), and 1-Butyl-3-methylimidazolium (BMIM), and of the anions Tetrafluoroborate (BF4), and Dicyanamide (DCA), using computer simulations. The structure and thermodynamics of the protein-IL interactions were evaluated by means of minimum-distance distribution functions (MDDFs) and the Kirkwood-Buff (KB) theory of solvation using the ComplexMixtures (http://m3g.iqm.unicamp.br/ComplexMixtures) software. The cooperativity of the interactions of the ions with the protein stems from the necessary electrical neutrality of the bulk solution. Specifically, the counterions' KB integrals are identical despite their contrasting interactions with the protein surface. Therefore, varying the hydrophobicity of the cation or the chemical nature of the anion implies different distributions of the corresponding counterions in the solution. The DCA anion, by forming hydrogen bonds to the protein surface, can drive the cations to the proximity of the protein surface. This effect is localized in the first two or three solvation shells of the protein. Direct correlations of the positions of the ions by alternating density augmentations can be observed at specific protein surface sites. At the same time, the protein can become preferentially hydrated by increasing the hydrophobicity of the cation and its concentration, independently of the strength of the interactions of the anion with the protein surface. In summary, cooperative ion effects determine the strength of the interactions of each component of the solution with the protein and the final solubility, and stability, of the biomolecules. Tuning the properties of ILs for specific applications rely on the understanding of these many-component effects.