Governments worldwide are taking actions to address the construction sector's sustainability concerns, including high carbon emissions, health and safety risks, low productivity, and increasing costs. Applying Industry 4.0 technologies to construction (also referred to as Construction 4.0) could address some of these concerns. However, current understanding about this is quite limited, with previous work being largely fragmented and limited both in terms of technologies as well as their interrelationships with the triple bottom line of sustainability perspectives. The focus of this study is therefore on addressing these gaps by i) proposing a comprehensive multidimensional Construction 4.0 sustainability framework that identifies and categorizes the key Construction 4.0 technologies and their positive and negative impacts on environmental, economic, and social sustainability, and then ii) establishing its applicability/usefulness through an empirical, multi-methodology case study assessment of the UAE's construction sector. The findings indicate Construction 4.0's positive impacts on environmental and economic sustainability far outweigh its negative effects, though these impacts are comparable with regards to social sustainability. On Construction 4.0 technologies itself, their application was found to be non-uniform, with greater application seen for building information modeling and automation vis-à-vis others such as cyber-physical systems and smart materials, with significant growth expected in the future for blockchain-and 3D-printing-related technologies. The proposed novel framework could enable the development of policy interventions and support mechanisms to increase Construction 4.0 deployment while addressing its negative sustainability-related impacts. The framework also has the potential to be adapted and applied to other country and sectoral contexts.