Abstract We present an Extreme Ultraviolet (EUV) transient grating (TG) experiment of the spinel Co3O4 compound using tuneable incident energies across the Co M2,3-edge and a 395 nm probe pulse, detecting both the first and the second diffraction orders. While the first diffraction order shows a monotonous behaviour as a function of time, with a sharp response at t=0, followed by a weak sub-picosecond component and a nearly constant signal thereafter, the time dependence of second diffraction order varies dramatically with the incident energy as it is tuned across the Co M-edge, with the appearance of a component at t>1 ps that grows with increasing energy. The results are rationalised in terms of the deviations of the initial grating from sinusoidal to non-sinusoidal, namely a flattening of the grating pattern, that introduces new Fourier components. These deviations are due to higher order, three-body terms in the population relaxation kinetics. These results highlight the use of the response of the second diffraction order in EUV TG as a tool to identify higher order terms in the population kinetics.