In order to measure tungsten isotopic composition in presolar stardust grains that contain a limited number of atoms, we developed a new three-photon three-color resonance ionization scheme using titanium:sapphire lasers and the Laser Ionization of Neutrals (LION) instrument at Lawrence Livermore National Laboratory. The first two transitions can be easily saturated, while approximately 84% of available atoms can be ionized in the third transition with our current laser irradiance. When ionizing from the ground state, measurements demonstrate a W useful yield of 14.4% +/- 1.6%. Experiments that intentionally cover a range of laser power and wavelength to simulate potential variations during analysis show that laser-induced W isotopic fractionation, if it occurs, is within measurement error. Overall, this new W resonance ionization scheme can be employed in future studies of atom limited samples to obtain W isotopic measurements.