We present an extreme ultraviolet (EUV) transient grating (TG) experiment of the spinel Co₃O₄ compound using tuneable incident energies across the Co M_2,3-edge and a 395 nm probe pulse, detecting both the first and the second diffraction orders (SDOs). While the first diffraction order shows a monotonous behavior 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 SDO 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 rationalized 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. The present results highlight the use of the SDO response in EUV TG as a tool to identify higher order terms in the population kinetics.