When new deliverables are added to the schedule just before the deadline, I will assess their impact on the already scheduled tasks, resources, and quality. The new deliverable is prioritized based on importance and feasibility; then, with stakeholders, adjust expectations, timelines, or resources.
In a worst-case scenario, I re-allocate the resources or reduce the scope of lesser critical tasks in order not to jeopardize the project's success. Communication of the change among the team members and stakeholders has to be done clearly.