Dialog modeling of making suggestions in human-agent interaction is a challenge due to the socially delicate nature of a suggestion and ensuing interactional negotiations. A basic first dialog model for making suggestions was tested in the context of schedule management assistance by an embodied conversational agent with elderly and mildly cognitively impaired persons. Analysis showed that users responded according to human social structures with most response types bearing potential challenges concerning the system's language understanding and the users' intention interpretation:next to explicit answers, users produced implicit versions for acceptance or resistance and further requests for information or modifications. Thus, an enhanced dialog model with a newly added clarification sequence and a new multi-conditional entry sequence was tested in a second study with the autonomous system. Initial observations show a promising performance of the dialog model.