Zero-shot multi-label recognition (MLR) with Vision-Language Models (VLMs) faces significant challenges without training data, model tuning, or architectural modifications. Existing approaches require prompt tuning or architectural adaptations, limiting zero-shot applicability. Our work proposes a novel solution treating VLMs as black boxes, leveraging scores without training data or ground truth. Using large language model insights on object co-occurrence, we introduce compound prompts grounded in realistic object combinations. Analysis of these prompt scores reveals VLM biases and AND''/OR'' signal ambiguities, notably that maximum compound scores are surprisingly suboptimal compared to second-highest scores. We address these through a debiasing and score-fusion algorithm that corrects image bias and clarifies VLM response behaviors. Our method enhances other zero-shot approaches, consistently improving their results. Experiments show superior mean Average Precision (mAP) compared to methods requiring training data, achieved through refined object ranking for robust zero-shot MLR.