A lot of recent work has studied strategies related to bulk loading of large data sets into multidimensional index structures. In this paper, we address the problem of bulk insertions into existing index structures with particular focus on R-trees — which are an important class of index structures used widely in commercial database systems. We propose a new technique, which as opposed to the current technique of inserting data one by one, bulk inserts entire new incoming datasets into an active R-tree. This technique, called GBI (for Generalized Bulk Insertion), partitions the new datasets into sets of clusters and outliers, constructs an R-tree (small tree) from each cluster, identifies and prepares suitable locations in the original R-tree (large tree) for insertion, and lastly performs the insertions of the small trees and the outliers into the large tree in bulk. Our experimental studies demonstrate that GBI does especially well (over 200% better than the existing technique) for randomly located data as well as for real datasets that contain few natural clusters, while also consistently outperforming the alternate technique in all other circumstances.