A doubly latent residual approach (DLRA) is presented to explain latent specific factors in multilevel bifactor-(S-1) models. The new approach overcomes some important limitations of the multiple indicators multiple causes (MIMIC) approach and allows researchers to predict latent specific factors at different levels. The DLRA is illustrated using real data from a large-scale assessment study. Furthermore, the statistical performance and power of the DLRA is examined in a Monte Carlo simulation study. The results show that the new DLRA performs well if more than 50 clusters and more than 10 observations per cluster are sampled. The power to test structural parameters at level 2 was lower than at level 1. To test a medium effect at level 2, we recommend to sample at least 100 clusters with a minimum cluster size of 10. The advantages and limitations of the new approach are discussed and guidelines for applied researchers are provided.