Use of directional antennas in cellular wireless networks offers many advantages such as range extension, reduced interference for signal detection and improved throughput. Recently, MAC protocols using directional antennas for wireless ad hoc networks that are based on and similar to IEEE 802.11 type WLANs have been proposed. In this paper, we explore ?multiplexing in space? with directional antennas to enhance the total throughput at a bottleneck node in the network. We develop an access protocol for antenna systems that can transmit to multiple destinations simulataneously (and possibly receive from multiple sources as well). Some issues enabling multiple access in space for ad hoc network nodes are discussed. Our simulation results show that the current 802.11 MAC scheme using omnidirectional antennas for channel access fairs very poorly as the bandwidth demand increases. In contrast, we see substantial improvement when spatial multiplexing is employed.