1. To support or attempt to placate both sides of a conflict or dispute. Many have criticized the US government of holding with the hare and running with the hound regarding the territorial dispute between the two nations.

2. To act duplicitously or hypocritically; to speak or act out against something while engaging or taking part in it. How can you be taken seriously as an anti-drug reformer when extensive documents reveal that you are a frequent user of methamphetamine? You can't hold with the hare and run with the hound, Senator.