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Texas Senator John Cornyn is in the running for Republican leader of the U.S. Senate. South Dakota's John Thune and Florida's Rick Scott are also interested in the gig. They're looking to replace Kentucky's Mitch McConnell, who is stepping aside as Republican leader in the Upper Chamber. Thune told CNBC he believes it would be in President-elect Donald Trump's best interest not to get involved in the race. Senate Republicans will hold the election for the party's new leader next Wednesday.