We investigate experimentally the possibility of enhancing the production of \(2^3S\) positronium atoms by driving the \(1^3S\)-\(3^3P\) and \(3^3P\)-\(2^3S\) transitions, overcoming the natural branching ratio limitation of spontaneous decay from \(3^3P\) to \(2^3S\). The decay of \(3^3P\) positronium atoms towards the \(2^3S\) level has been effciently stimulated by a 1312.2nm broadband IR laser pulse. The dependence of the stimulating transition efficiency on the intensity of the IR pulse has been measured to find the optimal enhancement conditions. A maximum relative increase of \( \times (3.1 \pm 1.0) \) in the \(2^3S\) production efficiency, with respect to the case where only spontaneous decay is present, was obtained.