Non-invasive marks, including pigmentation patterns, acquired scars, and genetic markers, are often used to identify individuals in mark-recapture experiments. If animals in a population can be identified from multiple, non-invasive marks then some individuals may be counted twice in the observed data. Analyzing the observed histories without accounting for these errors will provide incorrect inference about the population dynamics. Previous approaches to this problem include modeling data from only one mark and combining estimators obtained from each mark separately assuming that they are independent. Motivated by the analysis of data from the ECOCEAN online whale shark (Rhincodon typus) catalog, we describe a Bayesian method to analyze data from multiple, non-invasive marks that is based on the latent-multinomial model of Link et al. (2010, Biometrics 66, 178–185). Further to this, we describe a simplification of the Markov chain Monte Carlo algorithm of Link et al. (2010, Biometrics 66, 178–185) that leads to more efficient computation. We present results from the analysis of the ECOCEAN whale shark data and from simulation studies comparing our method with the previous approaches.