This paper describes generalizations of the MUSIC and root-MUSIC algorithms for direction of arrival (DOA) estimation to arrays composed of multiple translated subarrays. The advantage of these new approaches is that the DOAs can be estimated using either a one-dimensional search or by rooting a polynomial, as opposed to a multidimensional search as required by the multiple invariance (MI)-ESPRIT algorithm. While MI-MUSIC and root-MI-MUSIC are not statistically efficient like MI-ESPRIT, they do perform better than a single invariance implementation of ESPRIT, and are thus better suited for finding the initial conditions required by the MI-ESPRIT search.