Visual grouping -- operationalized through tasks such as instance segmentation, visual grounding, and object detection -- enables applications ranging from robotic perception to photo editing. These fundamental problems in computer vision are powered by large-scale, painstakingly annotated datasets. Despite their impact, these datasets are costly to build, biased in coverage, and difficult to scale. Synthetic datasets offer a promising alternative but struggle with flexibility, accuracy, and compositional diversity. We introduce Synthetic Object Compositions (SOC), an accurate and scalable data synthesis pipeline via a novel object-centric composition strategy. It composes high-quality synthetic object segments into new images using 3D geometric layout augmentation and camera configuration augmentation with generative harmonization and mask-area-weighted blending, yielding accurate and diverse masks, boxes, and referring expressions. Models trained on just 100K of our synthetic images outperform those trained on larger real datasets (GRIT 20M, V3Det 200K) and synthetic pipelines (Copy-Paste, X-Paste, SynGround, SegGen) by +24-36% -- achieving +10.9 AP on LVIS and +8.4 NAcc on gRefCOCO. Beyond the general open-vocabulary setup, SOC also enables controllable dataset construction for different use cases and boosts performance in both low-data and closed-vocabulary scenarios. Augmenting LVIS and COCO with synthetic object segments delivers strong performance across different real-data scales and yields even greater improvements under extremely limited real-data conditions, including +6.59 AP on a 1% COCO data setup. Furthermore, this controllability enables targeted data generation for intra-class referring, a diagnostic grounding task we propose that requires fine-grained attribute discrimination.