The phylogenetic inference package GCtree uses abundance of sampled sequences to improve the performance of parsimony-based inference, using a branching process model. Our previous work showed that GCtree performs competitively on B-cell receptor data, compared with other similar tools. In this article, we describe recent enhancements to GCtree, including an efficient tree storage data structure that discovers additional diversity of parsimonious trees with negligible additional computational cost. We also describe a suite of new objective functions that can be used to rank these trees, including a Poisson context likelihood function that models sequence evolution in a context-sensitive way. We validate these additions to GCtree with simulated B-cell receptor data, and benchmark performance against other phylogenetic inference tools.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.