With the wide availability of whole-genome genotype data, there is an increasing need for conducting genetic genealogical searches efficiently. Computationally, this task amounts to identifying shared DNA segments between a query individual and a very large panel containing millions of haplotypes. The celebrated Positional Burrows-Wheeler Transform (PBWT) data structure is a pre-computed index of the panel that enables constant time matching at each position between one haplotype and an arbitrarily large panel. However, the existing algorithm (Durbins Algorithm 5) can only identify set-maximal matches, the longest matches ending at any location in a panel, while in real genealogical search scenarios, multiple good enough matches are desired.