This paper studies matching of fragmented objects to recompose their original geometry. Solving this geometric reassembly problem has direct applications in archaeology and forensic investigation in the computer-aided restoration of damaged artifacts and evidence. We develop a new algorithm to effectively integrate both guidance from a template and from matching of adjacent pieces' fracture-regions. First, we compute partial matchings between fragments and a template, and pairwise matchings among fragments. Many potential matches are obtained and then selected/refined in a multi-piece matching stage to maximize global groupwise matching consistency. This pipeline is effective in composing fragmented thin-shell objects containing small pieces, whose pairwise matching is usually unreliable and ambiguous and hence their reassembly remains challenging to the existing algorithms.