<b>Background</b> <p>In the Nearest-Neighbor Thermodynamic Model, a standard approach for RNA secondary structure prediction, the energy of the multiloops is modeled using a linear entropic penalty governed by three branching parameters. Although these parameters are typically fixed, recent work has shown that reparametrizing the multiloop score and considering alternative branching conformations can lead to significantly better structure predictions. However, prior approaches for exploring the alternative branching structures were computationally inefficient for long sequences.</p> <b>Results</b> <p>We present a novel algorithm that partitions the parameter space, identifying all distinct branching structures (optimal under different branching parameters) for a given RNA sequence using the fewest possible minimum free energy computations. Our method efficiently computes the full parameter-space partition and the associated optimal structures, enabling a comprehensive evaluation of the structural landscape across parameter choices. We apply this algorithm to the Archive II benchmarking dataset, assessing the maximum attainable prediction accuracy for each sequence under the reparameterized multiloop model. We find that the potential for improvement over default predictions is substantial in many cases, and that the optimal prediction accuracy is highly sensitive to auxiliary modeling decisions, such as the treatment of lonely base pairs and dangling ends.</p> <b>Conclusion</b> <p>Our results support the hypothesis that the conventional choice of multiloop parameters may limit prediction accuracy and that exploring alternative parameterizations is both tractable and worthwhile. The efficient partitioning algorithm we introduce makes this exploration feasible for longer sequences and larger datasets. Furthermore, we identify several open challenges in identifying the optimal structure.</p>