A process to create composite preforms and parts by stacking layers of two-dimensional fiber material (e.g., fiber cloth, fiber reinforced fabric, etc.) having pin-receiving holes and/or gaps disposed between the fibers of the fiber material is described. The stack is pinned together using a subset of pins, such as fiber reinforcing pins, inserted into a subset of the pin receiving holes and/or gaps, leaving at least some of the pin receiving holes and/or gaps available for pinning other layers, as layers of fiber material are added to the stack. As additional layers are added to the stack, different subsets of pins connect the additional layers to the stack, thereby building up the stack. Each layer of fiber material may have a different shape than the other layers and any arbitrary topology, potentially including non-convex and/or disjoint shapes. Furthermore, implementations may produce composite preforms having an arbitrary number of interconnected layers.