Understanding how humans cooperatively rearrange household objects is critical for VR/AR and human-robot interaction. However, in-depth studies on modeling these behaviors are under-researched due to the lack of relevant datasets. We fill this gap by presenting CORE4D, a novel large-scale 4D human-object-human interaction dataset focusing on collaborative object rearrangement, which encompasses diverse compositions of various object geometries, collaboration modes, and 3D scenes. With 1K human-object-human motion sequences captured in the real world, we enrich CORE4D by contributing an iterative collaboration retargeting strategy to augment motions to a variety of novel objects. Leveraging this approach, CORE4D comprises a total of 11K collaboration sequences spanning 3K real and virtual object shapes. Benefiting from extensive motion patterns provided by CORE4D, we benchmark two tasks aiming at generating human-object interaction: human-object motion forecasting and interaction synthesis. Extensive experiments demonstrate the effectiveness of our collaboration retargeting strategy and indicate that CORE4D has posed new challenges to existing human-object interaction generation methodologies.