The high cost of obtaining high-quality annotated data for in-context learning (ICL) has motivated the development of methods that use self-generated annotations in place of ground-truth labels. While these approaches have shown promising results in few-shot settings, they generally do not scale to many-shot scenarios. In this work, we study ICL with self-generated examples using a framework analogous to traditional semi-supervised learning, consisting of annotation generation, demonstration selection, and in-context inference. Within this framework, we propose a simple baseline that outperforms ground-truth ICL in zero-shot, few-shot, and many-shot settings. Notably, we observe a scaling law with this baseline, where optimal performance is achieved with more than 1,000 demonstrations. To fully exploit the many-shot capabilities of semi-supervised ICL, we introduce IterPSD, an iterative annotation approach that integrates iterative refinement and curriculum pseudo-labeling techniques from semi-supervised learning, yielding up to 6.8% additional gains on classification tasks.