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The Super Proton Synchrotron (SPS) at CERN is the injector of the Large Hadron Collider (LHC). Multi-bunch instabilities limit the intensity of the beam that can be accelerated to 450 GeV in the SPS and transferred to the LHC. Without mitigation measures, the threshold of bunch intensity of the longitudinal instability is three times below the nominal bunch intensity of the LHC beam. The High Luminosity LHC project (HL-LHC), which requires a doubling of the nominal bunch intensity, relies on improvement of beam stability in the SPS. A fourth harmonic RF system allows, presently, to stabilize the beam up to nominal LHC intensity. It increases the synchrotron frequency spread inside the bunch, providing more efficient Landau damping of beam instability. However, nonlinearities of the synchrotron frequency distribution inside the bunch pose a limitation on bunch length. This paper explores possible intensity increase in the SPS by studying the effect on beam stability of the voltage ratio between two RF systems. The results are substantiated by beam measurements and particle-tracking simulations. An optimized voltage program of the second RF system during the cycle has been tested in operation and beam stability and the quality have been successfully improved. [ABSTRACT FROM AUTHOR]