The authors propose an additional level of parallelism, called multi-associativity, as a framework for simultaneously performing associative computation on data sets mapped to irregular, non-uniform, aggregates of processing elements (PEs). They introduce algorithms developed for the CAAPP to simulate efficiently within aggregates of PEs simultaneously the associative algorithms typically supported in hardware at the array level. Some of the results are: the efficient application of existing associative algorithms to arbitrary aggregates of PEs in parallel and the development of multi-associative algorithms, among them parallel prefix and convex hull. The multi-associative framework also extends the associative paradigm by allowing operation on and among aggregates themselves, operations not defined when the entity in question is always an entire array.>