Large Language Models (LLMs) are reshaping organizational knowing by unsettling the epistemological foundations of representational and practice-based perspectives. We conceptualize LLMs as Haraway-ian monsters, that is, hybrid, boundary-crossing entities that destabilize established categories while opening new possibilities for inquiry. Focusing on analogizing as a fundamental driver of knowledge, we examine how LLMs generate connections through large-scale statistical inference. Analyzing their operation across the dimensions of surface/deep analogies and near/far domains, we highlight both their capacity to expand organizational knowing and the epistemic risks they introduce. Building on this, we identify three challenges of living with such epistemic monsters: the transformation of inquiry, the growing need for dialogical vetting, and the redistribution of agency. By foregrounding the entangled dynamics of knowing-with-LLMs, the paper extends organizational theory beyond human-centered epistemologies and invites renewed attention to how knowledge is created, validated, and acted upon in the age of intelligent technologies.