Transcript assembly (i.e., to reconstruct the full-length expressed transcripts from RNA-seq data) has been a critical but yet unsolved step in RNA-seq analysis. Modern RNA-seq protocols can produce paired-/multiple-end RNA-seq reads, where information is available that two or more reads originate from the same transcript. The long-range constraints implied in these paired-/multiple-end reads can be much beneficial in correctly phasing the complicated spliced isoforms. However, there often exist gaps among individual ends, which may even contain junctions, making the efficient use of such constraints algorithmically challenging. Here we introduce Scallop2, a new reference-based transcript assembler optimized for multiple-end (including paired-end) RNA-seq data. Scallop2 uses an algorithmic framework that first represents reads from the same molecule as the so-called multiple-end phasing paths in the context of a splice graph, then bridges each multiple-end phasing path into a long, single-end phasing path, and finally decomposes the splice graph into paths (i.e., transcripts) guided by the bridged phasing paths. An efficient bridging algorithm is designed to infer the true path connecting two consecutive ends following a novel formulation that is robust to sequencing errors and transcript noises. By observing that failing to bridge two ends is mainly due to incomplete splice graphs, we propose a new method to determine false starting/ending vertices of the splice graphs which has been showed efficient in reducing false positive rate. Evaluations on both (multiple-end) single-cell RNA-seq datasets from Smart-seq3 protocol and Illumina paired-end RNA-seq samples demonstrate that Scallop2 vastly outperforms recent assemblers including StringTie2, Scallop, and CLASS2 in assembly accuracy.