<p>This paper advises and examines a strongly convergent relaxed bi-inertial Tseng’s extragradient method for approximating solutions to split variational inequality problems with multiple output sets. In our convergence results, we made no assumption about the sum condition on the iteration parameters, which differs from several existing results in this direction. The method employs variable step sizes that are modified at each iteration and depend on the results of previous iterations. This method has the advantage of requiring no prior knowledge of both the Lipschitz constant and the line search process. A series of numerical experiments was conducted to validate the efficacy and superiority of the presented iterative technique over existing methods in this area. The experiment confirms the effectiveness of the proposed algorithm for split variational inequality problems with multiple output sets in real Hilbert spaces.</p>