Primordial non-Gaussianity is a promising window onto the physics of the early universe. There is a huge discovery potential with excellent data from the Planck satellite expected soon. There may be a lot of information encoded in non-Gaussianity, and in particular I will motivate why it is worth studying correlators beyond the bispectrum (the 3-point function). Spatial inhomogeneities of the 3-point function on the CMB are a signal of non-zero higher-order correlators (for example the trispectrum); I will show under which cases this effect may be observable and how one may also use this effect to discriminate between models in which only one field (e.g. a curvaton) generates the primordial density perturbation, and those with multiple sources.