Cohesive subgraph discovery is an important problem in bipartite graph mining. In this paper, we focus on one kind of cohesive structure, called $k$-biplex, where each vertex of one side is disconnected from at most $k$ vertices of the other side. We consider the large maximal $k$-biplex enumeration problem which is to list all those maximal $k$-biplexes with the number of vertices at each side at least a non-negative integer $\theta$. This formulation, we observe, has various applications and targets to find non-redundant results by excluding non-maximal ones. Existing approaches suffer from massive redundant computations and can only run on small and moderate datasets. Towards improving scalability, we propose an efficient tree-based algorithm with two advanced strategies and powerful pruning techniques. Experimental results on real and synthetic datasets show the superiority of our algorithm over existing approaches.