Alzheimer's disease patients typically present with multiple co-morbid neuropathologies at autopsy, but the impact of these pathologies on cognitive impairment during life is poorly understood. In this study, we developed cognitive trajectories for patients with common co-pathologies in the presence and absence of Alzheimer's disease neuropathology. Cognitive trajectories were modelled in a Bayesian hierarchical regression framework to estimate the effects of each neuropathology on cognitive decline as assessed by the mini-mental state examination and the clinical dementia rating scale sum of boxes scores. We show that both TDP-43 proteinopathy and cerebral amyloid angiopathy associate with cognitive impairment of similar magnitude to that associated with Alzheimer's disease neuropathology. Within our study population, 63% of individuals given the 'gold-standard' neuropathological diagnosis of Alzheimer's disease in fact possessed either TDP-43 proteinopathy or cerebral amyloid angiopathy of sufficient severity to independently explain the majority of their cognitive impairment. This suggests that many individuals diagnosed with Alzheimer's disease may actually suffer from a mixed dementia, and therapeutics targeting only Alzheimer's disease-related processes may have severely limited efficacy in these co-morbid populations.