Methods, apparatus, systems, and computer-readable media are provided for tailoring composite graphical assistant interfaces for interacting with multiple different connected devices. The composite graphical assistant interfaces can be generated in response to a user providing a request for an automated assistant to cause a connected device to perform a particular function. In response to the automated assistant receiving the request, the automated assistant can identify other functions that the connected device is capable of performing. The other functions can then be mapped to various graphical control elements in order to provide a composite graphical assistant interface from which the user can interact with the connected device. Each graphical control element can be arranged according to a status of the connected device, in order to reflect how the connected device is operating simultaneous to the presentation of the composite graphical assistant interface.