Recently, Gaussian Splatting (GS) has received a lot of attention in surface reconstruction. However, while 3D objects can be of complex and diverse shapes in the real world, existing GS-based methods only limitedly use a single type of splatting primitive (Gaussian ellipse or Gaussian ellipsoid) to represent object surfaces during their reconstruction. In this paper, we highlight that this can be insufficient for object surfaces to be represented in high quality. Thus, we propose a novel framework that, for the first time, enables Gaussian Splatting to incorporate multiple types of (geometrical) primitives during its surface reconstruction process. Specifically, in our framework, we first propose a compositional splatting strategy, enabling the splatting and rendering of different types of primitives in the Gaussian Splatting pipeline. In addition, we also design our framework with a mixed-primitive-based initialization strategy and a vertex pruning mechanism to further promote its surface representation learning process to be well executed leveraging different types of primitives. Extensive experiments show the efficacy of our framework and its accurate surface reconstruction performance.