In this paper we introduce a general elliptical multivariate regression model in which the mean vector and the scale matrix have parameters (or/and covariates) in common. This approach unifies several important elliptical models, such as nonlinear regressions, mixed-effects model with nonlinear fixed effects, errors-in-variables models, and so forth. We discuss maximum likelihood estimation of the model parameters and obtain the information matrix, both observed and expected. Additionally, we derived the generalized leverage as well as the normal curvatures of local influence under some perturbation schemes. An empirical application is presented for illustrative purposes.