This article provides an analysis — within the framework of Radical Construction Grammar — of how BECOME developed into a copula ‘become’ out of an original sense ‘arrive’, and WAX, originally ‘grow’, also came to be used as a copula ‘become’. Importantly, it explains why these verbs successfully became fully productive copulas in a very short period of time. It is argued that this happened after a pre-copular stage had reached a cognitive threshold value. The occurrence of this threshold is related to the fact that the copular constructions featuring BECOME and WAX were not the end result of a single diachronic lineage of constructions (i.e. one construction developed out of another one, one at a time). Instead, the copularization of these verbs was the result of an interaction between lineages of constructions, belonging to two groups: (i) constructions involving BECOME or WAX, which gradually changed and interacted with each other; (ii) constructions involving already existing copulas, notably WEORÐAN ‘become’, which provided a generally productive analog upon which the newly emerging copulas could graft. Generally, the article calls attention to the importance of multiple source constructions and thresholds in understanding grammaticalization processes and productivity.