During cell division, crosslinking motors determine the architecture of the spindle, a dynamic microtubule network that segregates the chromosomes. It is unclear how motors with opposite directionality coordinate to drive both contractile and extensile behaviors in the spindle. Particularly, the impact of different crosslinker designs on network self-organization is not understood, limiting our understanding of self-organizing structures in cells, but also our ability to engineer new active materials. Here, we use experiment and theory to examine active microtubule networks driven by mixtures of motors with opposite directionality and different crosslinker design. We find that although the kinesin-14 HSET causes network contraction when dominant, it can also assist the opposing kinesin-5 KIF11 to generate extensile networks. This bifunctionality results from HSET’s asymmetric design, distinct from symmetric KIF11. These findings expand the set of rules underlying patterning of active microtubule assemblies and allow a better understanding of motor cooperation in the spindle.SIGNIFICANCE STATEMENTDuring cell division, the spindle apparatus segregates duplicated chromosomes for their inheritance by the daughter cells. The spindle is a highly interconnected network of microtubule filaments that are crosslinked by different types of molecular motors. How the different motors cooperate to organize the spindle network is not understood. Here, we show that an asymmetric crosslinker design can confer bifunctionality to a mitotic motor in the presence of other motors. The asymmetric motor supports both extensile and contractile microtubule network behaviors as observed in different parts of the spindle. These findings define new rules controlling the generation of active microtubule networks and allow us to better understand how motors cooperate to organize the correct spindle architecture when a cell divides.