A new aggregation approximation procedure is presented for analyzing single class closed queueing networks with simultaneous resource possession. It is applicable to multiple entry systems such as I/O models and relies on a new multi-entrance queue to aggregate the subnetwork with simultaneous resource possession into a variable rate queue. The resulting network is solved using conventional product form techniques. The multi-entrance queue has a service rate function that depends on the utilization of the primary resources of the subnetwork which enables calculation of the delay due to queueing for a specific resource, even when others are available. It has a product form solution, different from the solution currently known. A major advantage of the procedure is that the aggregation can be reversed to obtain estimates of low level performance parameters once the solution is obtained. A solution algorithm is presented along with two examples. Results are compared with simulation models.