To open the access of the scientific community to expensive computing resources, the resource providers deploy sometimes more than one grid middleware on the respective resources. The complexity of developing applications capable of operating in heterogeneous grids currently scales with the number of different middleware and services available. In addition to the challenge of hiding the technical complexity of the grid, the grid applications face now an additional challenge, namely hiding the heterogeneity of the grid middleware (different standards and protocols for job management, file management e.g.). In this work we present our experiences with the integration in the GridSTEA framework of the support for resource and management from the Globus Toolkit 4 and 5 and from gLite 3.2 middleware. The resulting application has modules that can be used as is by any grid application developer. We consider such experiences valuable in the perspective of the unification of the grid middleware stack, the European approach that puts together services and products stemming from all major middleware software.