Bidirectional changes over time in the estimated glomerular filtration rate and in urine protein content are of interest for the treatment and management of patients with lupus nephritis. Although these processes may be modelled by separate multistate models, the processes are likely to be correlated within patients. Motivated by the lupus nephritis application, we develop a new multistate modelling framework where subject-specific random effects are introduced to account for the correlations both between the processes and within patients over time. Models are fitted by using bespoke code in standard statistical software. A variety of forms for the random effects are introduced and evaluated by using the data from the Systemic Lupus International Collaborating Clinics.