Marine diatoms are important primary producers that can undergo multitrait changes in response to environmental or demographic perturbations. Here, we investigated how flexible multitrait correlations are over hundreds of generations, and how lineage diversity and phenotype diversity are related. We used a perturbation-evolution experiment with Thalassiosira diatoms in which they were 'knocked-off' their ancestral multitrait phenotype peak using repeated population bottlenecks, and were then allowed to grow unhindered as large populations. We found that most multitrait phenotypes were isolated but that in 10% of cases, phenotypes were connected by viable trajectories. Following the bottleneck perturbation, evolving in a +4 degrees Celsius environment favoured the discovery of novel multitrait phenotypes, while evolving in the ancestral environment most often resulted in the ancestral phenotype re-evolving. Finally, both trait values and trait correlations evolved in this experiment, with the most drastic changes in trait correlations being associated with lower growth rates. Our findings demonstrate that demographic events that result in decreases in fitness, such as population bottlenecks, have the potential to play an important role in the realised connectivity of phenotypes, as well as in shaping the relationship between lineage and phenotypic diversity in diatoms.