In order to explore the role of enhanced spin-orbit interactions on the laser-induced ultrafast magnetization dynamics, we performed a comparative study on cobalt thin films and Co/Pt multilayers. We show that the presence of the Co/Pt interfaces gives rise to a three-fold faster demagnetization upon femtosecond laser heating. Experimental data for a wide range of laser fluences are analyzed using the Microscopic 3-Temperature Model. We find that the Elliott-Yafet spin-flip scattering in the multilayer structure is increased by at least a factor of four with respect to the elementary Co film.