Representing human-made objects as a collection of base primitives has a long history in computer vision and reverse engineering. In the case of high-resolution point cloud scans, the challenge is to be able to detect both large primitives as well as those explaining the detailed parts. While the classical RANSAC approach requires case-specific parameter tuning, state-of-the-art networks are limited by memory consumption of their backbone modules such as PointNet++, and hence fail to detect the fine-scale primitives. We present Cascaded Primitive Fitting Network (CPFN) that relies on an adaptive patch sampling network to assemble detection results of global and local primitive detection networks. As a key enabler, we present a merging formulation that dynamically aggregates the primitives across global and local scales. Our evaluation demonstrates that CPFN improves the state-of-the-art SPFN performance by 13-14% on high-resolution point cloud datasets and specifically improves the detection of fine-scale primitives by 20-22%.