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A Computer-Aided Design (CAD) model encodes an object in two coupled forms: a \emph{parametric construction sequence} and its resulting \emph{visible geometric shape}. During iterative design, adjustments to the geometric shape inevitably require synchronized edits to the underlying parametric sequence, called \emph{geometry-driven parametric CAD editing}. The task calls for 1) preserving the original sequence’s structure, 2) ensuring each edit's semantic validity, and 3) maintaining high shape fidelity to the target shape, all under scarce editing data triplets. We present \emph{CADMorph}, an iterative \emph{plan–generate–verify} framework that orchestrates pretrained domain-specific foundation models during inference: a \emph{parameter-to-shape} (P2S) latent diffusion model and a \emph{masked-parameter-prediction} (MPP) model. In the planning stage, cross-attention maps from the P2S model pinpoint the segments that need modification and offer editing masks. The MPP model then infills these masks with semantically valid edits in the generation stage. During verification, the P2S model embeds each candidate sequence in shape-latent space, measures its distance to the target shape, and selects the closest one. The three stages leverage the inherent geometric consciousness and design knowledge in pretrained priors, and thus tackle structure preservation, semantic validity, and shape fidelity respectively. Besides, both P2S and MPP models are trained without triplet data, bypassing the data-scarcity bottleneck. CADMorph surpasses GPT-4o and specialized CAD baselines, and supports downstream applications such as iterative editing and reverse-engineering enhancement.