San Francisco’s top governing body will spend time on Tuesday discussing what most residents surely would not consider a major priority for the city: whether Julie Park and Tom McDonald can raise the roof of their $2.1 million Victorian home by 7 feet and 3 inches.

The project complies with city codes, and the San Francisco Planning Commission gave unanimous approval months ago; in many cities that would have been good enough for the remodel to move forward. But in San Francisco, neighbors wield unusual power over next-door renovations and modest improvements and can appeal even the replacement of rotted front steps.

So on Tuesday, 11 members of San Francisco’s Board of Supervisors will serve as judges in home construction, hearing from Ms. Park and Mr. McDonald, their neighbors, lawyers, Planning Department experts and any members of the public who care to weigh in.

The feud between wealthy neighbors is emblematic of the city’s languor when it comes to building anything. San Francisco has already drawn the ire of state housing officials, who have demanded that the city add 82,000 units in the next seven years, a goal that seems out of reach when many projects draw multiple rounds of challenges and years of delays.

“This isn’t to say that other California cities don’t have similar planning battles royale, but historically speaking, San Francisco has distinguished itself as the leader of the pack,” Dan Sider, chief of staff for the San Francisco Planning Department, said.

Ms. Park, a 40-year-old consultant for start-ups and small businesses, began her quest during the pandemic when she and Mr. McDonald, a 38-year-old climate researcher, bought their three-story home on Harper Street on the edge of Noe Valley in 2020. The neighborhood is popular with families and close to hilltop hikes that provide stunning views.