The law became the center of national debate after George Zimmerman used the defense in the shooting death of Trayvon Martin.
One of the suggested changes, an extension of legal liability, was criticized by some lawmakers, the South Florida Sun-Sentinel reported.
The provision would make a person acting in self-defense liable when they negligently injure or kill a bystander.
"What we're saying is we're putting them in jeopardy even if they're trying to defend themselves," said Sen. John Thrasher, R-St. Augustine, who voted against the bill.
The lawmaker who drafted the bill that became law in 2005, Sen. David Simmons, R-Altamonte Springs, praised the law, but said it needed some changes.
"I think everyone has found it is an excellent, common sense law," he said. "But it is not perfect."
He said the modifications offered by the bill would protect innocent bystanders harmed by someone acting with "negligence," such as spraying bullets in the air.
The bill also would require local law enforcement to set guidelines for neighborhood watch programs, and limit their activities to observing and reporting crime.
People who are the "aggressors" in a confrontation would be barred from using "stand your ground" as a defense under the legislation. Police would be required to conduct a full investigation of incidents in which "stand your ground" is claimed.
Simmons' bill is being combined with a similar proposal filed by Senate Majority Leader Chris Smith, D-Fort Lauderdale. Differences in the bills must still be worked out.
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