Large Language Models (LLMs) fail at reasoning when their parametric knowledge is outdated or incorrect. A common solution for mitigating outdated or incorrect information in models is to provide updated facts in-context or by knowledge editing, but such updates can conflict with LLMs' parametric knowledge and limit their reasoning. Current benchmarks for this problem, however, largely focus only on single knowledge updates and fact recall in isolated scenarios. In this work, we introduce TКЂбґЂбґ„бґ‹ (Testing Reasoning Amid Conflicting Knowledge), a new benchmark for studying how LLMs propagate new knowledge through multi-step reasoning when it conflicts with the model's initial parametric knowledge. Spanning three reasoning-intensive scenarios (WIKI, CODE, and MATH), TКЂбґЂбґ„бґ‹ introduces multiple, realistic conflicts to mirror real-world complexity. Our results on TКЂбґЂбґ„бґ‹ reveal that providing updated facts yields limited performance gains and even worsens performance, compared with no facts provided. Performance further degrades with more updated facts. This failure stems from both inability to faithfully integrate updated facts and flawed reasoning even when knowledge is integrated. TКЂбґЂбґ„бґ‹ provides a rigorous new benchmark to measure and guide future progress on propagating conflicting knowledge in multi-step reasoning.