The pattern of trace element enrichment and variability found in differentiated suites of basalts is a simple observable, which nonetheless records a wealth of information on processes occurring from the mantle to crustal magma chambers. The incompatible element contents of some mid-ocean ridge basalt (MORB) sample suites show progressive enrichment beyond the predictions of simple models of fractional crystallization of a single primary melt. Explanations for this over-enrichment have focused on the differentiation processes in crustal magma chambers. Here we consider an additional mechanism and focus instead on the deviation from simple fractionation trends that is possible by mixing of diverse mantle-derived melts supplied to magma chambers. A primary observation motivating this strategy is that there is significant chemical diversity in primitive high-MgO basalts, which single liquid parent models cannot match. Models were developed to simulate the compositional effects of concurrent mixing and crystallization (CMC): diverse parental melts were allowed to mix, with a likelihood that is proportional to the extent of fractional crystallization. Using a simple statistical model to explore the effects of concurrent mixing and crystallization on apparent liquid lines of descent, we show how significant departure from Rayleigh fractionation is possible as a function of the diversity of trace elements in the incoming melts, their primary MgO content, and the relative proportion of enriched to depleted melts. The model was used to make predictions of gradients of trace element enrichment in log[trace element]–MgO space. These predictions were compared with observations from a compilation of global MORB and provide a test of the applicability of CMC to natural systems. We find that by considering the trace element variability of primitive MORB, their MgO contents and degree of enrichment, CMC accurately predicts the pattern of trace element over-enrichment seen in global MORB. Importantly, this model shows that the relationship between over-enrichment and incompatibility can result from mantle processes: the fact that during mantle melting maximum variability is generated in those elements with the smallest bulk $Kd$. Magma chamber processes are therefore filtering the signal of mantle-derived chemical diversity to produce trace element over-enrichment during differentiation. Finally, we interrogate the global MORB dataset for evidence that trace element over-enrichment varies as a function of melt supply. There is no correlation between over-enrichment and melt supply in the global dataset. Trace element over-enrichment occurs at slow-spreading ridges where extensive steady-state axial magma chambers, the most likely environment for repeated episodes of replenishment, tapping and crystallization, are very rarely detected. This supports a model whereby trace element over-enrichment is an inevitable consequence of chemically heterogeneous melts delivered from the mantle, a process that may operate across all rates of melt supply.