The aggregation of the amyloid β peptide (Aβ42), which is linked to Alzheimer's disease, can be altered significantly by modulations of the peptide's intermolecular electrostatic interactions. Variations in sequence and solution conditions have been found to lead to highly variable aggregation behaviour. Here we modulate systematically the electrostatic interactions governing the aggregation kinetics by varying the ionic strength of the solution. We find that changes in the solution ionic strength induce a switch in the reaction pathway, altering the dominant mechanisms of aggregate multiplication. This strategy thereby allows us to continuously sample a large space of different reaction mechanisms and develop a minimal reaction network that unifies the experimental kinetics under a wide range of different conditions. More generally, this universal reaction network connects previously separate systems, such as charge mutants of the Aβ42 peptide, on a continuous mechanistic landscape, providing a unified picture of the aggregation mechanism of Aβ42.