Large language models (LLMs) have shown remarkable performance across various sentence-based linguistic phenomena, yet their ability to capture cross-sentence paradigmatic patterns, such as verb alternations, remains underexplored. In this work, we present curated paradigm-based datasets for four languages, designed to probe systematic cross-sentence knowledge of verb alternations (change-of-state and object-drop constructions in English, German and Italian, and Hebrew binyanim). The datasets comprise thousands of the Blackbird Language Matrices (BLMs) problems. The BLM task -- an RPM/ARC-like task devised specifically for language -- is a controlled linguistic puzzle where models must select the sentence that completes a pattern according to syntactic and semantic rules. We introduce three types of templates varying in complexity and apply linguistically-informed data augmentation strategies across synthetic and natural data. We provide simple baseline performance results across English, Italian, German, and Hebrew, that demonstrate the diagnostic usefulness of the datasets.