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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,\footnote{In this paper, we use `bilingual corpora' to denote parallel corpora with `bilingual translation pairs' in many different language pairs, each consisting of two sentences/documents with the same meaning written in different languages. We use `trilingual corpora' to denote parallel corpora with `trilingual translation pairs' in many different language combinations, each consisting of three sentences/documents.} and sometimes synthetic document-level bilingual corpora. This hampers the performance with cross-lingual document-level tasks such as document-level translation. Therefore, we propose to mine and leverage document-level trilingual parallel corpora to improve sequence-to-sequence multilingual pre-training. We present \textbf{Tri}angular Document-level \textbf{P}re-training (\textbf{TRIP}), which is 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.