Can Ahri's ultimate cause her Orb of Deception to trigger more than twice?

Solution 1:

League of Legends has two types of blinks - "true" blinks, like the summoner spell flash, and "Blinkdash"es, skills like Poppy's Heroic Charge, Xin Zhao's Audacious Charge, and Ahri's Spirit Rush.

The big difference is that blinkdashes don't remove the champion from the field. If you Blinkdash through a skillshot, you will still get hit by the skill shot.

In Ahri's case, this means as soon as she tries to dash over her orb, she will simply pick it back up instead.

What you propose would be possible with the summoner spell Flash (similar feats have been done with Sivir's Boomerang Blade), but the paltry damage is probably not worth wasting flash's long cooldown on.