The ageing population has caused a marked increased in the number of people with cognitive decline linked with dementia. Thus, current diagnostic services are overstretched, and there is an urgent need for automating parts of the assessment process. In previous work, we demonstrated how a stratification tool built around an Intelligent Virtual Agent (IVA) eliciting a conversation by asking memory-probing questions, was able to accurately distinguish between people with a neuro-degenerative disorder (ND) and a functional memory disorder (FMD). In this paper, we extend the number of diagnostic classes to include healthy elderly controls (HCs) as well as people with mild cognitive impairment (MCI). We also investigate whether the IVA may be used for administering more standard cognitive tests, like the verbal fluency tests. A four-way classifier trained on an extended feature set achieved 48% accuracy, which improved to 62% by using just the 22 most significant features (ROC-AUC: 82%).