LLM jailbreaks are a widespread safety challenge. Given this problem has not yet been tractable, we suggest targeting a key failure mechanism: the failure of safety to generalize across semantically equivalent inputs. We further focus the target by requiring desirable tractability properties of attacks to study: explainability, transferability between models, and transferability between goals. We perform red-teaming within this framework by uncovering new vulnerabilities to multi-turn, multi-image, and translation-based attacks. These attacks are semantically equivalent by our design to their single-turn, single-image, or untranslated counterparts, enabling systematic comparisons; we show that the different structures yield different safety outcomes. We then demonstrate the potential for this framework to enable new defenses by proposing a Structure Rewriting Guardrail, which converts an input to a structure more conducive to safety assessment. This guardrail significantly improves refusal of harmful inputs, without over-refusing benign ones. Thus, by framing this intermediate challenge - more tractable than universal defenses but essential for long-term safety - we highlight a critical milestone for AI safety research.