System identification provides many convenient and useful methods for engineering modelling. This study targets the parameter identification problems for multivariable equation-error autoregressive moving average systems. To reduce the influence of the coloured noises on the parameter estimation, the data filtering technique is adopted to filter the input and output data, and to transform the original system into a filtered system with white noises. Then the filtered system is decomposed into several subsystems and a filtering-based partially-coupled generalised extended stochastic gradient algorithm is developed via the coupling concept. In contrast to the multivariable generalised extended stochastic gradient algorithm, the proposed algorithm can give more accurate parameter estimates. Finally, the effectiveness of the proposed algorithm is well demonstrated by simulation examples.