When Congress put a $10,000 cap on the amount of state and local taxes individuals can deduct from their federal income taxes, high-tax states tried to fight for their residents in a couple of different ways.

One way—charitable funds that earned people state tax credits for donations—got shot down by the IRS.

But states have tried another kind of workaround. Because the deduction cap applies only to individuals, not to businesses, some states have instituted new taxes on pass-through businesses,...