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Direct species interactions are commonly included in individual fitness models used for coexistence and local diversity modeling. Though widely considered important for such models, direct interactions alone are often insufficient for accurately predicting fitness, coexistence, or diversity outcomes. Incorporating higher-order interactions (HOIs) can lead to more accurate individual fitness models but also adds many model terms, which can quickly result in model overfitting. We explore approaches for balancing the trade-off between tractability and model accuracy that occurs when HOIs are added to individual fitness models. To do this, we compare models parameterized with data from annual plant communities in Australia and Spain, varying in the extent of information included about the focal and neighbor species. The best-performing models for both data sets were those that grouped neighbors based on origin status and life form, a grouping approach that reduced the number of model parameters substantially while retaining important ecological information about direct interactions and HOIs. Results suggest that the specific identity of focal or neighbor species is not necessary for building well-performing fitness models that include HOIs. In fact, grouping neighbors by even basic functional information seems sufficient to maximize model accuracy, an important outcome for the practical use of HOI-inclusive fitness models.