Residents would vote to fill the three school board spots that represent their district, rather than voting for all nine positions, as they do now.
The district, which has almost 12,000 students, is one of about two dozen in the area whose board is composed entirely of at-large members who can live anywhere in the district.
Any new map would need to be approved by Pennsylvania Common Pleas Court. The voting regions could be in effect in time for next year's primary elections, depending on how quickly the map wins court approval, district officials said.
Residents in the district have argued for and against the new system, with each side citing politics as a driving factor in the change.
The electoral committee began public meetings in February to discuss a change. The map on which the school board declined to vote Monday was one of four the committee considered.
The four board members elected in November had said they would explore regionalization if elected.
School board member Maureen Snook said she was glad the board delayed its vote.
"Now, there will be more time for discussion and time to put together a specific plan of how this is going to affect people," she said.
The board members in favor of the change want to make sure future boards represent the diversity of the district, said Rob Partridge, the district's spokesman.
Opponents of the change cite the district's own 30-year analysis of the makeup of the board, which shows no apparent evidence that board members came from any particular area more often than from others. They say the district should stay whole and argue that future board members will prioritize their regions when they make decisions.
While opponents say smaller voting regions would limit the pool of candidates, supporters say the change would make running for school board easier.
Val DiGiorgio, chair of the Chester County Republican Committee, called the change "a politically motivated scheme to redistrict."
Stephanie Markstein, one of the West Chester Borough Democrats, said she would prefer a map that does not split up the borough. Board members in favor of the map said splitting several municipalities was inevitable in order to have uniform populations in the three regions. Still, Markstein said, she favors regionalization over the current system. "We're trying to keep the politics out of the school board race as much as possible," she said.
Throughout the state, about 36 percent of school districts have regional boards, 60 percent are at-large, and 4 percent are a combination, according to statistics the Pennsylvania School Boards Association released in 2012.