Big History provides a very powerful framework for understanding the broad contours of the past, from the beginning of the Universe at the Big Bang to our present globe-spanning information-based technological civilization. But to what degree can this framework also be used to draw potential insights into the contours of the possible future of humanity, as it emerges from the complex dynamics of the present? In this paper, we make use of the '8-threshold' formulation of Big History due to David Christian and examine some of the conceptual possibilities that arise when we consciously and systematically take a 'Big History perspective' on the future of humanity at the global scale. Specifically, we consider the question of what the next major threshold in Big History---what we might therefore call 'Threshold 9'---may look like in broad outline. We find that, of the four main 'generic' categories of possible futures, the most probable global future currently in prospect---barring a major catastrophic shock, technological energy breakthrough, or similar low-probability 'wildcard' event---is a slowly-unfolding collapse or 'descent' over a time-scale of decades-to-centuries towards a human society characterized by ever-declining access to sources of fossil-fuel-based energy. Such a future trajectory clearly has major implications for the level of human societal complexity possible. This suggests undertaking an anticipatory program of continuing research and exploration into both the underlying nature and the emergent characteristics of the coming transition to 'Threshold 9'.