Bytewise approximate matching algorithms have in recent years shown significant promise in de- tecting files that are similar at the byte level. This is very useful for digital forensic investigators, who are regularly faced with the problem of searching through a seized device for pertinent data. A common scenario is where an investigator is in possession of a collection of "known-illegal" files (e.g. a collection of child abuse material) and wishes to find whether copies of these are stored on the seized device. Approximate matching addresses shortcomings in traditional hashing, which can only find identical files, by also being able to deal with cases of merged files, embedded files, partial files, or if a file has been changed in any way. Most approximate matching algorithms work by comparing pairs of files, which is not a scalable approach when faced with large corpora. This paper demonstrates the effectiveness of using a "Hierarchical Bloom Filter Tree" (HBFT) data structure to reduce the running time of collection-against-collection matching, with a specific focus on the MRSH-v2 algorithm. Three experiments are discussed, which explore the effects of different configurations of HBFTs. The proposed approach dramatically reduces the number of pairwise comparisons required, and demonstrates substantial speed gains, while maintaining effectiveness.