In order to improve TCP performance, a method using a PEP (Performance Enhancing Proxy) is proposed. In the method, the PEP is located in a intermediate router along a TCP connection. When a data packet arrives at the PEP, it forwards the packet, stores the copy of the packet into its own buffer (PEP buffer), and returns the corresponding ACK (premature ACK) in behalf of the destination host. In previous researches, under the strategy which keeps the number of the packets in the PEP buffer for which premature ACKs have been returned being less than or equal to a fixed threshold value (watermark value), we have investigated the relation between the watermark value and throughput when only one TCP connection exists. In this paper, under the above strategy, we investigate the relation between the watermark value and the maximum throughput when multiple TCP connections exist. Simulation results under the assumption that each connection uses a dedicated PEP buffer show that the average throughput of each connection is nearly equal to each other regardless of the watermark value. We also show that the relation between the watermark value and throughput is the same as that when only one connection exists.