Signalling requires precise spatial and temporal regulation of molecular interactions, which is frequently orchestrated by disordered scaffolding proteins, such as A-kinase anchoring protein 5 (AKAP5). AKAP5 contains multiple Short Linear Motifs (SLiMs) that assemble the necessary components, including the phosphatase Calcineurin, which is anchored via a well-characterised PxIxIT SLiM. Here we show, using a combination of biochemical and biophysical approaches, that Calcineurin also recognises additional lower-affinity SLiMs C-terminal to the PxIxIT motif. Moreover, we demonstrate that the assembly is in reality a complex system in which AKAP SLiMs spanning a wide affinity range act cooperatively to maintain distinct pools of anchored and more loosely held enzyme, analogous to the well-understood transcription factor search complexes on DNA, and compatible with the requirement for both stable anchoring and responsive downstream signalling. We conclude that the AKAP5 C-terminus is enriched in lower-affinity/mini-SLiMs that cooperate to maintain a structurally disordered but tightly regulated signalosome.