Multi-agent reinforcement learning (MARL) has emerged as a promising paradigm for adaptive traffic signal control (ATSC) of multiple intersections. Existing approaches typically follow either a fully centralized or a fully decentralized design. Fully centralized approaches suffer from the curse of dimensionality, and reliance on a single learning server, whereas purely decentralized approaches operate under severe partial observability and lack explicit coordination resulting in suboptimal performance. These limitations motivate region-based MARL, where the network is partitioned into smaller, tightly coupled intersections that form regions, and training is organized around these regions. This paper introduces a Semi-Centralized Training, Decentralized Execution (SEMI-CTDE) architecture for multi intersection ATSC. Within each region, SEMI-CTDE performs centralized training with regional parameter sharing and employs composite state and reward formulations that jointly encode local and regional information. The architecture is highly transferable across different policy backbones and state-reward instantiations. Building on this architecture, we implement two models with distinct design objectives. A multi-perspective experimental analysis of the two implemented SEMI-CTDE-based models covering ablations of the architecture's core elements including rule based and fully decentralized baselines shows that they achieve consistently superior performance and remain effective across a wide range of traffic densities and distributions.