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Clonal lineage inference ("tumor phylogenetics") has become a crucial tool for making sense of somatic evolution processes that underlie cancer development and are increasingly recognized as part of normal tissue growth and aging. The inference of clonal lineage trees from single cell sequence data offers particular promise for revealing processes of somatic evolution in unprecedented detail. However, most such tools are based on fairly restrictive models of the types of mutation events observed in somatic evolution and of the processes by which they develop. The present work seeks to enhance the power and versatility of tools for single-cell lineage reconstruction by making more comprehensive use of the range of molecular variant types by which tumors evolve. We introduce Sc-TUSV-ext, an integer linear programming (ILP) based tumor phylogeny reconstruction method that, for the first time, integrates single nucleotide variants (SNV), copy number alterations (CNA) and structural variations (SV) into clonal lineage reconstruction from single-cell DNA sequencing data. We show on synthetic data that accounting for these variant types collectively leads to improved accuracy in clonal lineage reconstruction relative to prior methods that consider only subsets of the variant types. We further demonstrate the effectiveness on real data in resolving clonal evolution in the presence of multiple variant types, providing a path towards more comprehensive insight into how various forms of somatic mutability collectively shape tissue development.