<p>In this paper, we study the concept of bilevel variational inequality featuring strongly monotone variational inequality over the solution set of the split variational inequality problem with multiple output sets in real Hilbert spaces. We propose two new two-step inertial iterative methods with self-adaptive step sizes for approximating the problem’s solution in the framework of Hilbert spaces. Our proposed algorithms eliminate the dependence on the norm of the transformation operators and the strongly monotone and Lipschitz continuous constants of the involved operators. Furthermore, strong convergence results are obtained without the co-coerciveness of the associated single-valued operators. Finally, we apply our result to study certain classes of split inverse problems and we present several numerical experiments to demonstrate the implementability of the proposed method.</p>