The progression of tumours to malignancy is commonly considered to arise through lineal evolution, a process in which mutations conferring pro-oncogenic cellular phenotypes are acquired by a succession of ever-more dominant clones. However, this model is at odds with the persistent polyclonality observed in many cancers. We propose that an alternative mechanism for tumour progression, called interclonal cooperativity, is likely to play a role at stages of tumour progression when mutations cause microenvironmental changes, such as occur with epithelial-mesenchymal transitions (EMTs). Interclonal cooperativity occurs when cancer cell-cancer cell interactions produce an emergent malignant phenotype from individually non-malignant clones. In interclonal cooperativity, the oncogenic mutations occur in different clones within the tumour that complement each other and cooperate in order to drive progression. This reconciles the accepted genetic and evolutionary basis of cancers with the observed polyclonality in tumours. Here, we provide a conceptual basis for examining the importance of cancer cell-cancer cell interactions to the behaviour of tumours and propose specific mechanisms by which clonal diversity in tumours, including that provided by EMTs, can drive the progression of tumours to malignancy.