Hydrogen peroxide, H2O2, acts as a particularly strong reactant in aqueous environment. It has been demonstrated earlier that agglomerates with a single peroxide interacting with one and two water molecules manifest in several stable conformers within a narrow energy range. In the present study we seek structural changes brought out by adding an extra H2O2 to these systems at molecular level employing ab initio quantum chemical methods, viz., restricted Hartree-Fock and the second order Moller-Plesset perturbation theory. These clusters exhibit consistent trends in energy hierarchy at both the levels. Further, a many body interaction energy analysis quantifies the strength and cooperativity of hydrogen bonding in the (H2O2)2...(H2O)n, (n=1 and 2) clusters, bringing out structuring/destructuring effects attributed to attachment of water and hydrogen peroxide molecules.