Gov. Andrew Cuomo wants to overhaul the state tax system by swapping state income for payroll taxes, which remain deductible under the new federal tax code.

But lawmakers are already offering up their own alternative ideas, including measures to “decouple” the state tax deductions from the federal rules.

At least three bills, from Westchester Democratic Assemblywoman Amy Paulin, Brooklyn Democratic Sen. Simcha Felder and Senate Independent Democratic Conference member David Carlucci, would accomplish this.

Underlying their proposed bills is a phenomenon that has drawn scant attention but which could cost New Yorkers millions in additional taxes if not addressed.

State income tax deductions in New York largely conform to the federal rules. Because of that, state income taxes, like their federal counterparts, are now subject to a $10,000 cap on local property tax deductions.

Unless New York changes its tax code, lots of New Yorkers would get a double hit  — since they would face the new $10,000 limit on both state and federal taxes.

That could be remedied by language saying New York doesn’t adhere to the new laws or by simply saying state rules follow federal rules as of 2017, rather than 2018 when the new federal code took effect.

The loss of state deductibility could cost taxpayers an estimated $400 million, noted E.J. McMahon, research director of the Empire Center, a fiscal watchdog group. He blogged about this potential increase earlier in January, calling it a “stealth tax hike.”

Also unaddressed is the loss of exemptions by single filers who claim themselves as exemptions.

Those exemptions have gone away under the new federal tax code.

Because New York also piggybacks on that rule, some 5.2 million single people could end up paying an additional $840 million in state taxes, according McMahon, who noted that state Department of Taxation and Finance estimates have pointed this out as well.

This could be changed easily, he said, by altering the language in the governor’s budget proposal.

“It’s inexplicable,” McMahon said of Cuomo’s failure to highlight the issue in his budget presentation earlier this month. “All they had to do was insert it in the law.”

State Budget spokesman Morris Peters said they will likely address those issues in their 30-day amendments to Cuomo’s plan to swap income and payroll taxes.

He said they didn’t have the time to address all the aspects of state tax law  between the Dec. 22, 2017, signing of the federal tax changes and Cuomo’s Jan. 16 budget speech.

McMahon, though, has his doubts since state officials were aware of other details tucked into the federal tax bill such as an expansion of a child tax credit, which was decoupled from the state rules.

Paulin and Felder, who caucuses with the Republicans, have recently offered “decoupling” bills.

And Carlucci back in May proposed legislation that does away with state deductibility caps.

Members of Congress back then began seriously talking about eliminating or capping state and local deductions.

“This is just a common sense bill,” Carlucci said.

The bills, along with remarks by Senate Republican Majority Leader John Flanagan, suggest that Cuomo’s plan to allow swapping payroll and income taxes may be part of a broader discussion.

“Before we look at federal tax reform we should look at how we are doing things in the state of New York,” Flanagan said Monday on the Capitol Pressroom radio show.

While not hitting a majority of wage-earning New Yorkers, Cuomo has described the $10,000 cap on state and local deductions as an economic missile that Republican President Donald Trump and the GOP-led Congress has hurled at high-tax Democratic states like New York.

The fear is the loss of deductions for those who own expensive, highly taxed homes in places like Westchester County, New York City and Long Island, will drive many people out of the state and deplete New York’s budget coffers.

Income tax receipts from Westchester, New York City and Long Island make up a disproportionate share of the state budget.