Premiums could rise up to 84 percent for new Palm Beach County customers of state-run Citizens Property Insurance Corp. under a bill on the Florida Senate’s special order calendar today.

The bill would uncap rates for new customers and raise the annual rate cap on the company’s existing 1.3 million customers — including about 130,000 in Palm Beach County — from 10 percent to 13 percent. The extra money would be used to buy more private reinsurance from offshore and Wall Street interests.

That means annual bills for families with existing Citizens policies could go up 13 percent a year, not just 10 percent, in addition to any other increases they may face because of inspections that stripped credits for such storm-resistant features as shutters. Supporters say spending more on private reinsurance could reduce the need for later assessments on Citizens customers and others if the state is hit by, say, a once-a-century megastorm. Chance of that happening in any given year: 1 percent.

Another wrinkle under the bill: Gov. Rick Scott and Florida Chief Financial Officer Jeff Atwater would directly appoint the company’s executive director, a job Citizens officials said refers to the post held by company President and CEO Barry Gilway.

Asked whether Scott supports these moves, deputy press secretary John Tupps said: “The governor wants to keep the cost of living low for Florida families while reducing the risk of all home and auto insurance policy holders paying a hurricane tax in the event of a major storm. Any final legislation the governor signs must meet both of these goals.”

The bill has good points, including a clearinghouse to help consumers find options besides Citizens, but also plenty of bad ones, said Jay Neal, executive director of the Florida Association for Insurance Reform, a group that says it represents policyholders and others affected by insurance changes.

“The bad provisions include making the Citizens president and CEO a direct political appointee of the governor and CFO, as if Citizens needs to be more political not less,” Neal wrote in a letter to newspapers. He said the bill would “weaken the Citizens board” and restrict the authority of the state’s Office of Insurance Regulation to review and approve rates.

Citizens President Gilway, speaking before the Senate’s Banking and Insurance Committee Tuesday, acknowledged a number of territories “would see rate increases over 60 percent.” According to Citizens records, territories facing possible increases above 60 percent include three coastal areas of Palm Beach County.

Gilway said if rates increased to what Citizens considered adequate around the state, the increases could be even higher in some instances. For example, he said a homeowner’s premium in an area with sinkholes, such as Hernando County, might rise from $3,000 a year to about $9,000.

The bill would allow Citizens to set rates for new customers at higher levels based on its assessment of the risk or, in some places, pegged to a formula designed to set its rates higher than those of private insurers.

Sen. Jeff Clemens, D-Lake Worth, asked whether the calculations include what people can afford. New customers could include not just someone building a home but also any family whose private insurer simply dropped them, as has happened to hundreds of thousands of homeowners in South Florida. He questioned how many people could afford to stay in their homes with such increases.

“We’re talking about putting people out of their homes, right?” Clemens said Tuesday. “It’s not just about numbers. It’s about people’s livelihoods.”

Gilway said it was up to legislators to decide how to carry out the changes, though he noted customers told him to his face how increases were affecting them at an insurance roundtable hosted by The Palm Beach Post last month.

“I had probably 10 to 12 couples lined up to talk to me after that presentation concerned about rate increases they’re facing,” Gilway said.

Sen. Garrett Richter, R-Naples, said existing Citizens customers would not see the larger increases, but the state should draw the line with new customers.

“I don’t think we should be be putting people in policies for $3,000 when it should cost $9,000,” Richter said.

The bill, SB 1770, could be considered as early as today or pushed off to a later date if the chamber focuses on budget issues and other matters. The House has no exact counterpart to the Senate’s package, though a bill with the clearinghouse, for example, is on second reading there.

In other action, the Senate Banking and Insurance Committee put off a vote on repealing on the state’s no-fault car insurance system as Chairman David Simmons said he wanted to talk more with the governor and key House members.