This talk concerns the construction of Cauchy initial data whose future development gives rise to multiple causally independent trapped regions. The results include both the vacuum Einstein equations and the Einstein-Maxwell-Klein-Gordon system for collapsing boson stars, as well as a construction with prescribed ADM energy, linear momentum, and angular momentum for each component. I will focus on the main geometric picture, the relation between the different constructions, and the role of recent developments in gluing techniques in making these results possible. This is based on joint work with Dawei Shen and Elena Giorgi.