Morel & Nagaraj (1993) proposed a finite mixture distribution for modelling multinomial extra variation when the extra variation is believed to be caused by clumped multinomial sampling with one clumping. We propose an extension of the model to incorporate possible multiple clumping. We show that the extended finite mixture distribution is a multinomial mixing distribution with different mixing coefficients. We derive maximum likelihood estimating equations and an asymptotic approximation to the Fisher information matrix for the parameters of the model. A real-life dataset is analysed.