I've wondered about this, but for a little different reason. Say my main carrier is mostly into auto industry and I take a load to GM in Kansas City, not much on the way of auto parts coming back. But if I have connections with another carrier with a broader load base it might get me a back haul quicker.
That's the theory, and it's what is behind the myth of being leased on to multiple carriers means having less down time. It's the exception to the rule, because the overwhelming number of carriers who allow multiple leases are all bidding on the same freight in the same manner, and do not have a broader load base. Those with a broader load base are not likely to allow their contractors to lease with another company. That's why the notion of being leased on with multiple carriers will get you more freight ends up being a self-deluded myth, in most cases. You end up with the same amount of freight, and usually at a lower rate.
If you are able to selectively pick and choose 2 or 3 carriers who each have different customer bases and methods of obtaining freight, then it's doable. For example, if you are on with 3 carriers, only one could be part of Sylectus, and the other two would have to have their own unique customer bases which are not part of the Sylectus market. Doing this is not easy and requires considerable knowledge of the industry, or an insane amount of luck.