Escalation analysis in the space domain has been dominated by linear, binary, and threshold-based models often tied to the space-nuclear nexus. While this literature has generated valuable insights, it fails to capture the prevailing nature of conflict in space, and as such, the complexity of the escalation dynamics that underlie it. Currently, conflicts in the space domain occur in the form of sub-threshold campaigns, which are non-kinetic and ambiguous but at the same time persistent and strategically consequential, even without directly threatening nuclear systems. This paper ventures to understand how escalation takes shape in the context of these subthreshold operations. It draws on the dynamical systems theory to advance a novel theoretical framework for analysing escalation risk across cyber, electronic warfare, directed energy, and proximity manoeuvres. The framework operationalises escalation risk through five stages: defining the system state, characterising action attributes, mapping vertical, horizontal, and cumulative escalation pathways, assessing composite risk, and identifying accelerants and dampeners of escalatory risk. The paper uses illustrative scenarios to demonstrate that low-intensity and reversible actions can generate significant escalation pressures through cross-domain spillover, norm erosion, and misperception, often overlooked in nuclear-centric models, which often emphasise linear ladder or spiral frameworks. The study contributes to escalation theory by emphasising non-linearity, state dependence, and cumulative dynamics. It offers a structured tool for policymakers and military planners to anticipate and manage escalation risks in space.