Structural RNAs exhibit a vast array of recurrent short three-dimensional (3D) elements found in loop regions involving non-Watson–Crick interactions that help arrange canonical double helices into tertiary structures. Here we present CaCoFold-R3D, a probabilistic grammar that predicts these RNA 3D motifs (also termed modules) jointly with RNA secondary structure over a sequence or alignment. CaCoFold-R3D uses evolutionary information present in an RNA alignment to reliably identify canonical helices (including pseudoknots) by covariation. Here we further introduce the R3D grammars, which also exploit helix covariation that constrains the positioning of the mostly noncovarying RNA 3D motifs. Our method runs predictions over an almost-exhaustive list of over 50 known RNA motifs (‘everything’). Motifs can appear in any nonhelical loop region (including three-way, four-way and higher junctions) (‘everywhere’). All structural motifs as well as the canonical helices are arranged into one single structure predicted by one single joint probabilistic grammar (‘all-at-once’). Our results demonstrate that CaCoFold-R3D is a valid alternative for predicting the all-residue interactions present in a RNA 3D structure. CaCoFold-R3D is fast and easily customizable for novel motif discovery and shows promising value both as a strong input for deep learning approaches to all-atom structure prediction as well as toward guiding RNA design as drug targets for therapeutic small molecules.