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This work presents generalized low-rank signal decompositions with the aid of switching techniques and adaptive algorithms, which do not require eigen-decompositions, for space-time adaptive processing. A generalized scheme is proposed to compute low-rank signal decompositions by imposing suitable constraints on the filtering and by performing iterations between the computed subspace and the low-rank filter. An alternating optimization strategy based on recursive least squares algorithms is presented along with switching and iterations to cost-effectively compute the bases of the decomposition and the low-rank filter. An application to space-time interference suppression in DS-CDMA systems is considered. Simulations show that the proposed scheme and algorithms obtain significant gains in performance over previously reported low-rank schemes.