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Recently, an eigenvector-based algorithm has been developed for multidimensional frequency estimation with a single snapshot of data mixture. Unlike most existing algebraic approaches that estimate frequencies from eigenvalues, the eigenvector-based algorithm achieves automatic frequency pairing without joint diagonalization of multiple matrices, but it fails when there exist identical frequencies in certain dimensions because eigenvectors are not linearly independent anymore. In this paper, we develop an eigenvector-based algorithm for multidimensional frequency estimation with finite data snapshots. We also analyze the identifiability (ID) and performance of the proposed algorithm. It is shown that our algorithm offers the most relaxed statistical ID condition for multidimensional frequency estimation from finite snapshots. More important, we introduce complex weighting factors so that the algorithm is still operational when there exist identical frequencies in one or more dimensions. Furthermore, the weighting factors are optimized to minimize the mean square errors of the frequency estimates. Simulation results show that the proposed algorithm offers competitive performance when compared to existing algebraic approaches but at lower complexity.