Neural models are increasingly used in Web-scale Information Retrieval (IR). However, relying on these models introduces substantial computational and energy requirements, leading to increasing attention toward their environmental cost and the sustainability of large-scale deployments. While neural IR models deliver high retrieval effectiveness, their scalability is constrained in multi-domain scenarios, where training and maintaining domain-specific models is inefficient and achieving robust cross-domain generalisation within a unified model remains difficult. This paper introduces DRAMA (Domain Retrieval using Adaptive Module Allocation), an energy- and parameter-efficient framework designed to reduce the environmental footprint of neural retrieval. DRAMA integrates domain-specific adapter modules with a dynamic gating mechanism that selects the most relevant domain knowledge for each query. New domains can be added efficiently through lightweight adapter training, avoiding full model retraining. We evaluate DRAMA on multiple Web retrieval benchmarks covering different domains. Our extensive evaluation shows that DRAMA achieves comparable effectiveness to domain-specific models while using only a fraction of their parameters and computational resources. These findings show that energy-aware model design can significantly improve scalability and sustainability in neural IR.