American Airlines Inc.’s appellate win will undermine the stability of Texas’s chief business-tax system if allowed to stand, the comptroller told state justices in a petition for review.

The statewide appeals court that hears challenges to state laws held in April that federal Anti-Head Tax Act bars Texas from imposing franchise taxes on the company’s air transportation earnings. But the franchise tax isn’t a tax “on” gross receipts that falls under the act, but rather a “composite tax” that uses those gross receipts as part of the calculation of the taxpayer’s entire business, the state comptroller told the Texas Supreme …