The paper introduces a phylogenetic terrace aware (PTA) data structure to efficiently analyze supermatrices under partition models in phylogenomics. Partition models allow each gene or partition to evolve under its own evolutionary model, but missing data can lead to phylogenetic terraces, which hinder tree search algorithms. The PTA data structure exploits partial terraces and induced partition trees to save computation time. It is implemented in IQ-TREE and shown to achieve substantial speedups of up to 4.5 and 8 times compared to standard IQ-TREE and RAxML implementations, respectively, under different partition models. The PTA is applicable to all types of partition models and common topological rearrangements, making it a versatile tool for phylogenomic inference software. The authors also discuss the efficiency of the PTA in handling large alignments with missing data and provide a detailed analysis of its performance on real alignments.The paper introduces a phylogenetic terrace aware (PTA) data structure to efficiently analyze supermatrices under partition models in phylogenomics. Partition models allow each gene or partition to evolve under its own evolutionary model, but missing data can lead to phylogenetic terraces, which hinder tree search algorithms. The PTA data structure exploits partial terraces and induced partition trees to save computation time. It is implemented in IQ-TREE and shown to achieve substantial speedups of up to 4.5 and 8 times compared to standard IQ-TREE and RAxML implementations, respectively, under different partition models. The PTA is applicable to all types of partition models and common topological rearrangements, making it a versatile tool for phylogenomic inference software. The authors also discuss the efficiency of the PTA in handling large alignments with missing data and provide a detailed analysis of its performance on real alignments.