Head-and-neck cancer (HNC) planning is difficult because multiple critical organs-at-risk (OARs) are close to complex targets. Intensity-modulated carbon-ion therapy (IMCT) offers superior dose conformity and OAR sparing but remains slow due to relative biological effectiveness (RBE) modeling, leading to laborious, experience-based, and often suboptimal tuning of many treatment-planning parameters (TPPs). Recent deep learning (DL) methods are limited by data bias and plan feasibility, while reinforcement learning (RL) struggles to efficiently explore the exponentially large TPP search space. We propose a scalable multi-agent RL (MARL) framework for parallel tuning of 45 TPPs in IMCT. It uses a centralized-training decentralized-execution (CTDE) QMIX backbone with Double DQN, Dueling DQN, and recurrent encoding (DRQN) for stable learning in a high-dimensional, non-stationary environment. To enhance efficiency, we (1) use compact historical DVH vectors as state inputs, (2) apply a linear action-to-value transform mapping small discrete actions to uniform parameter adjustments, and (3) design an absolute, clinically informed piecewise reward aligned with plan scores. A synchronous multi-process worker system interfaces with the PHOENIX TPS for parallel optimization and accelerated data collection. On a head-and-neck dataset (10 training, 10 testing), the method tuned 45 parameters simultaneously and produced plans comparable to or better than expert manual ones (relative plan score: RL $85.93\pm7.85%$ vs Manual $85.02\pm6.92%$), with significant (p-value $<$ 0.05) improvements for five OARs. The framework efficiently explores high-dimensional TPP spaces and generates clinically competitive IMCT plans through direct TPS interaction, notably improving OAR sparing.