Alzheimer’s disease is a progressive neurodegenerative disorder marked by declining cognitive function. While early-stage treatment focuses on acetylcholinesterase (AChE) inhibition, butyrylcholinesterase (BChE) activity increases as the disease progresses, contributing to cholinergic deficits and neuroinflammation. This shift in enzyme dominance presents a compelling rationale for developing BChE-specific inhibitors as a potential therapeutic avenue. This study explores small, three-membered rings, scaffolds offering potential for interaction with the enzyme’s active site, as building blocks for novel BChE inhibitors. Employing a computational approach based on quantum–chemical multiligand simultaneous molecular docking, we virtually fitted these compounds into the BChE active site to predict binding affinity and key interactions. Our calculations extend beyond simple shape matching by incorporating accurate electronic properties, leading to more reliable predictions of binding strength and stability. The goal was not immediate identification of potent inhibitors, but a systematic assessment of how these rings interact with BChE. This foundational knowledge will inform the design and synthesis of larger, more complex molecules with enhanced binding affinity and selectivity, ultimately aiming to develop compounds to inhibit BChE activity and potentially slow Alzheimer’s progression.