The core-mantle boundary (CMB) is a complex and poorly understood region of the Earth. The existence of melt or partial melt at the CMB is strongly debated with evidence coming from a range of sources. While partial melt has been inferred in specific locations using seismology, often as an explanation for ultra-low velocity zones (ULVZs), no global layer of melt has been observed despite evidence that such melt should accumulate at the CMB. Using high frequency synthetic seismograms we have systematically examined the effect of a one-dimensional melt layer at the CMB on the global seismic wavefield. We find that PKKP diffracted waves are an extremely sensitive, robust and previously underutilised seismic phase for studying the CMB and, in synthetic testing, could resolve very thin melt layers. We have constructed a global data set of PKKP diffracted observations to attempt to observe or exclude melt at the CMB. We find that within the bounds of our data, we are unable to robustly exclude or observe a melt layer at the CMB on the order of single kilometres thick. The presence of a thin layer of unobservable melt at the CMB would have profound impacts for the internal dynamics of the Earth.