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This paper introduces a novel Bayesian model to estimate multi--quantiles in a dynamic framework. The main innovation relies on the assumption that the $\tau$--th level quantile of a vector of response variables depends on macroeconomic variables as well as on latent factors having their on stochastic dynamics. The proposed framework can be conveniently thought as a factor--augmented vector autoregressive extension of traditional univariate quantile models. We develop Bayesian methods that rely on state space representation and data augmentation approaches that efficiently deal with the estimation of model parameters and the signal extraction from latent variables. We estimate the model using a large panel of US equity market returns and macroeconomic variables to analyse the dynamic evolution of spillovers in individual Value--at--Risks.