In many commonly used models for multivariate traits, the likelihood is specified as a mixture of nested sums of products over the unobserved genotypes of all the family members, in which the familial covariance matrices vary in size and structure for different families, and their sizes can be immense for large family units. These issues pose computational difficulties in many applications. ... [Show full abstract] Bonney's compound regressive model for univariate traits simplifies the familial covariance structure and reduces the mixture of nested sums only to the parent-offspring level, thus enhancing computation significantly. This model has been extended to the multivariate case in the absence of unobserved genotypes. Here, we further extend this model to incorporate major genes, covariates and multiple loci. As is typical in practice, this causes new computational difficulties. We study the computational issues and explore the behaviour of this extended model. Copyright 2006 Royal Statistical Society.