This paper investigates the transmission capacity of open-loop spatial multiplexing with zero-forcing receivers in overlaid ad hoc networks. We first derive asymptotic closed-form expressions for the transmission capacity of two coexisting networks (a primary network vs. a secondary network). We then address a special case with equal numbers of transmit and receive antennas through exact analysis. Numerical results validate the accuracy of our expressions. Our findings show that the overall transmission capacity of coexisting networks will improve significantly over that of a single network if the primary network can tolerate a slight outage probability increase. This improvement can be further boosted if more streams are configured in the spatial multiplexing scheme; less improvement is achieved by placing more antennas at the receive side than the transmit side. However, when the stream number exceeds a certain limit, spatial multiplexing will produce negative effect for the overlaid network.