Implementations set forth herein relate to an automated assistant that is responsive to spoken utterances spoken by multiple different users simultaneously, or otherwise within a narrow window of time, in furtherance of initializing one or more actions. For instance, when a primary user is interacting with an automated assistant, a secondary user may also provide a spoken utterance. In response, the automated assistant can selectively determine whether any input from the secondary user should affect a request from the primary user. In some instances, the automated assistant can elect to either disregard the secondary input, separately respond to the secondary input, or use some amount of content of the secondary input to further the request from the primary user. Incorporation of secondary input when fulfilling a primary request can be fluidly performed to resemble human conversation and eliminate any unnecessary engagement between the automated assistant and the users.