You can’t do exactly that yet in native Asana (perhaps with flowsana.net, @Phil_Seeman?).
But you can achieve something similar with rules mimicking the task template you have. Rules can set values of fields, add subtasks with metadata set, etc., all things a task template does, just a different way.
@Kasey_Nichols’s answer describes this a bit with multi-homing, but you don’t require multi-homing to do the functions mentioned.
Hope that helps,
Larry