Since sequential patterns may exist in multiple sequence databases, we propose algorithm PropagatedMine+ to efficiently discover multi-domain sequential patterns. Prior works have shown that algorithm PropagatedMine outperforms other methods. In this paper, by exploring lattice structures, we develop algorithm PropagatedMine+ for propagating. Note that the lattice structure provides some guidelines when mining sequential patterns in other domain databases. Thus, exploiting the lattice structure devised could further reduce the number of candidate patterns, thereby improving the performance of mining sequential patterns across multiple domain sequence databases. A comprehensive performance study is conducted and experimental results show the scalability and the efficiency of algorithm PropagatedMine+.