We discuss inference for repeated fractional data, with outcomes between 0 to 1, including positive probability masses on 0 and 1. The point masses at the boundaries prevent the routine use of logit and other commonly used transformations of (0, 1) data. We introduce a model augmentation with latent variables that allow for the desired positive probability at 0 and 1 in the model. A linear mixed effect model is imposed on the latent variables. We propose a Bayesian semiparametric model for the random effects distribution. Specifically, we use a Polya tree prior for the unknown random effects distribution. The proposed model can capture possible multimodality and skewness of random effect distribution. We discuss implementation of posterior inference by Markov chain Monte Carlo simulation. The proposed model is illustrated by a simulation study and a cancer study in dogs.