Large language models (LLMs) exhibit reasoning biases, often conflating content plausibility with formal logical validity. This can lead to wrong inferences in critical domains, where plausible arguments are incorrectly deemed logically valid or vice versa. This paper investigates how content biases on reasoning can be mitigated through activation steering, an inference-time technique that modulates internal activations. Specifically, after localising the layers responsible for formal and plausible inference, we investigate activation steering on a controlled syllogistic reasoning task, designed to disentangle formal validity from content plausibility. An extensive empirical analysis reveals that contrastive steering methods consistently support linear control over content biases. However, a static approach is insufficient to debias all the tested models. We then investigate how to control content effects by dynamically determining the steering parameters through fine-grained conditional methods. By introducing a novel kNN-based conditional approach (K-CAST), we demonstrate that conditional steering can effectively reduce biases on unresponsive models, achieving up to 15% absolute improvement in formal reasoning accuracy. Finally, we found that steering for content effects is robust to prompt variations, incurs minimal side effects on multilingual language modeling capabilities, and can partially generalize to different reasoning tasks. In practice, we demonstrate that activation-level interventions offer a scalable inference-time strategy for enhancing the robustness of LLMs, contributing towards more systematic and unbiased reasoning capabilities.