Despite the success of multilingual sequence-to-sequence pre-training, most existing approaches rely on document-level monolingual corpora in many different languages, sentence-level bilingual corpora, and sometimes synthetic document-level bilingual corpora. This hampers the performance with cross-lingual document-level tasks such as document-level translation. Hence, we propose to mine and leverage document-level trilingual parallel corpora to improve sequence-to-sequence multilingual pre-training. We present Triangular Document-level Pre-training (TRIP) as the first in the field to accelerate the conventional monolingual and bilingual objectives into a trilingual objective with a novel method called Grafting. Experiments show that TRIP achieves several strong state-of-the-art (SOTA) scores on three multilingual document-level machine translation benchmarks and one cross-lingual abstractive summarization benchmark, including consistent improvements by up to 3.11 d-BLEU points and 8.9 ROUGE-L points.