In Multi-device or cross-device environments (XDEs), people can use face-to-face communication and coordination channels to build and maintain a shared understanding about the task at hand (known as communication grounding) during collaboration. Also, in XDEs, people's attention may be focused on personal devices for independent data exploration. Therefore, communication and coordination among team members may require extra effort. In this paper, I propose a method to analyze the cost of communication grounding in XDEs. I also propose two user studies to investigate the impact of digital support for coordinating a specific action, i.e. data transfer, on communication grounding in XDEs.