High penetration of renewable energy sources (RESs) induces sharply-fluctuating feeder power, leading to voltage deviation in active distribution systems. To prevent voltage violations, multi-terminal soft open points (M-SOPs) have been integrated into the distribution systems to enhance voltage control flexibility. However, the M-SOP voltage control recalculated in real-time cannot adapt to the rapid fluctuations of photovoltaic (PV) power, fundamentally limiting the voltage controllability of M-SOPs. To address this issue, a full-model-free adaptive graph deep deterministic policy gradient (FAG-DDPG) model is proposed for M-SOP voltage control. Specifically, the attention-based adaptive graph convolutional network (AGCN) is leveraged to extract the complex correlation features of nodal information to improve the policy learning ability. Then, the AGCN-based surrogate model is trained to replace the power flow calculation to achieve model-free control. Furthermore, the deep deterministic policy gradient (DDPG) algorithm allows FAG-DDPG model to learn an optimal control strategy of M-SOP by continuous interactions with the AGCN-based surrogate model. Numerical tests have been performed on modified IEEE 33-node, 123-node, and a real 76-node distribution systems, which demonstrate the effectiveness and generalization ability of the proposed FAG-DDPG model.