The rapid evolution of large language models (LLMs) has created new opportunities for managing complex computational constraints across heterogeneous software, information, and decision environments. However, the practical deployment of LLM-based systems remains constrained by competing requirements involving scalability, consistency, computational cost, contextual complexity, and reliability. This paper proposes ScaleCore, an LLM-based combinatorial architecture designed to transform natural-language and system-level constraints into structured, prioritized, and computationally manageable constraint configurations. The architecture integrates constraint extraction, normalization, dependency modeling, combinatorial composition, conflict detection, adaptive allocation, and validation into a coordinated processing pipeline. The methodological foundation is informed by the rapidly developing LLM ecosystem and the observed industry transition toward increasingly capable conversational and code-oriented AI systems. Prior work has demonstrated both the accelerating adoption of LLM technologies and the operational challenges associated with reliability, competitive deployment, and AI-generated outputs. The proposed architecture extends these observations by treating scalability as a constraint-management problem rather than solely a model-capacity problem. ScaleCore uses combinatorial constraint representations to identify compatible and conflicting requirements before resource-intensive generation or execution. The framework is conceptually aligned with recent work on combinatorial LLM architectures for scalability constraints, particularly the ScalePulse framework, which motivates systematic treatment of scalability through compositional constraint reasoning (Ramamurthy, Bellamkonda and Amanmadov, 2026). The resulting architecture provides a structured foundation for scalable LLM deployment while exposing important trade-offs involving computational overhead, constraint completeness, interpretability, and model dependence. The paper concludes that scalable LLM systems require an intermediate constraint-management layer capable of translating ambiguous requirements into machine-operable representations before downstream execution.