Summary. A conditionally Markov multiplicative intensity model is described for the analysis of clustered progressive multistate processes under intermittent observation. The model is motivated by a long-term prospective study of patients with psoriatic arthritis with the aim of characterizing progression of joint damage via an irreversible four-state model. The model accommodates heterogeneity in transition rates between different individuals and correlation in transition rates within patients. To do this we introduce subject-specific multivariate random effects in which each component acts multiplicatively on a specific transition intensity. Through the association between the components of the random effect, correlations in transition intensities are accommodated. A Monte Carlo EM algorithm is developed for estimation, which features closed form expressions for estimators at each M-step.