Model fairness (a.k.a., bias) has become one of the most critical problems in a wide range of AI applications. An unfair model in autonomous driving may cause a traffic accident if corner cases (e.g., extreme weather) cannot be fairly regarded; or it will incur healthcare disparities if the AI model misdiagnoses a certain group of people (e.g., brown and black skin). In recent years, there have been emerging research works on addressing unfairness, and they mainly focus on a single unfair attribute, like skin tone; however, real-world data commonly have multiple attributes, among which unfairness can exist in more than one attribute, called 'multi-dimensional fairness'. In this paper, we first reveal a strong correlation between the different unfair attributes, i.e., optimizing fairness on one attribute will lead to the collapse of others. Then, we propose a novel Multi-Dimension Fairness framework, namely Muffin, which includes an automatic tool to unite off-the-shelf models to improve the fairness on multiple attributes simultaneously. Case studies on dermatology datasets with two unfair attributes show that the existing approach can achieve 21.05% fairness improvement on the first attribute while it makes the second attribute unfair by 1.85%. On the other hand, the proposed Muffin can unite multiple models to achieve simultaneously 26.32% and 20.37% fairness improvement on both attributes; meanwhile, it obtains 5.58% accuracy gain.