Because of economic and operational advantages of consolidation, switch sizes continue to grow both in terms of call capacity and the number of voice circuits served. Because a good overload performance is critical for network and service integrity, it is important to find out whether there are any limitations on the size of the switch from an overload control perspective, i.e., whether the well-established internal overload control strategies continue to work well as the switch size increases. We study this question via a detailed simulation model, and discover there need not be any fundamental limitations on the switch size provided that the scheduling disciplines, buffer sizes, and peripheral scanning schemes are chosen properly, and the number of peripherals is not too large.