The PARAFAC2 decomposition has attracted growing research interest. To compute it, the direct fitting (DF) algorithm is usually employed. In this contribution, we propose to incorporate semi-algebraic approaches for the computation of PARAFAC in the DF algorithm and explore how it should be adapted to largely exploit the resulting diversity in the estimates of factor matrices to enhance the robustness and efficiency. Three versions have been tailored and recommended for different parameter settings according to, e.g., the number of components or tensor dimensions. Extensive numerical simulations have been conducted with both synthetic and measured biomedical as well as wine data to validate the improved performance of the proposed DF algorithms. In addition, it has been shown that applying the geometric search on top of the proposed DF algorithms further boosts their performance.