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“Is that a good idea? I don’t know,” Mr. Reddam said. “So you have to try stuff.”

But I’ll Have Another and the bright spotlight a potential Triple Crown would provide certainly aids the pursuit of so many around horse racing to make it more of a presence on the sporting landscape. That, Mr. Stevens said, will take time.

But at least for now, I’ll Have Another’s final stride down the stretch could be a step in the right direction.

“It would be a great boost for all of us,” Mr. Lukas said.