Summary: We fully compute the \(\mathcal N = 1\) supersymmetrization of the fourth power of the Weyl tensor in \(d = 4 \)x-space with the auxiliary fields. In a previous paper, we showed that their elimination requires an infinite number of terms; we explicitely compute those terms to order \(\kappa ^{4}\) (three loop). We also write, in superspace notation, all the possible \(\mathcal N = 1\) actions, in four dimensions, that contain pure \(\mathcal R^{4}\) terms (with coupling constants). We explicitely write these actions in terms of the \(\theta \) components of the chiral density \(\epsilon\) and the supergravity superfields \(R,G_{m},W_{ABC}\). Using the method of gauge completion, we compute the necessary \(\theta \) components which allow us to write these actions in \(x\)-space. We discuss under which circumstances can these extra \(\mathcal R^{4}\) correction terms be reabsorbed in the pure supergravity action, and their relevance to the quantum supergravity/string theory effective actions.