Intermediate-task training---fine-tuning a pretrained model on an intermediate task before fine-tuning again on the target task---often improves model performance substantially on language understanding tasks in monolingual English settings. We investigate whether English intermediate-task training is still helpful on non-English target tasks. Using nine intermediate language-understanding tasks, we evaluate intermediate-task transfer in a zero-shot cross-lingual setting on the XTREME benchmark. We see large improvements from intermediate training on the BUCC and Tatoeba sentence retrieval tasResearch goal: Does the performance gain from intermediate-task training in zero-shot cross-lingual transfer persist when scaling to larger, state-of-the-art multilingual models (e.g., Bloom, mBART) on XTREME-R, measured by accuracy across typologically diverse languages?Autonomous synthesis report generated by Assignee Research. Tribunal consensus score: 9.2/10.