Interval-censored time-to-event data often occur in studies of diseases where the symptoms of interest are not directly observable but require lab examinations for detection. Furthermore, the independence assumption among observations may not be valid if they are from clusters. Some methods have been developed for analysing clustered interval-censored data with a shared frailty to account for overall heterogeneity. In this paper, we propose a multiple frailty proportional hazards model, where we not only account for the baseline heterogeneity and effect variation across clusters for predictors, but also quantify the probabilities of the existence of such frailties. This proposed model will be especially useful for analysing multi-center randomised clinical trials for HIV, infections or progression-free survival in oncology studies.