In 2012, Penn and its developer won a zoning variance and demolition approval to erect a five-story, 122-unit apartment building.
But the Woodland Terrace Homeowners Association and two rental-property owners appealed in Common Pleas Court.
The neighborhood is zoned for single-family, duplexes or houses with special certificates for up to eight tenants.
"We are fighting for all the homeowners who live near Penn," said Mary Daniels, of Woodland Terrace. "Homeownership is an important stabilizer in West Philly, and the zoning court is meant to encourage that."
In a separate challenge, the Woodland Terrace group has also appealed the Historical Commission's demolition approval.
Two months ago, Weiss and Penn proposed a new plan to the Spruce Hill Community Association: Rather than demolish the mansion, they would erect an L-shaped building around it.
Community leaders believed that it was an attempt to end the legal battles.
Barry Grossbach, zoning chairman of Spruce Hill, said members who live on Pine Street liked the new project. But Woodland Terrace residents, who live south of Baltimore Avenue, rejected it.
"We are simply mystified at the failure to respond positively and to work with the new proposal that the developer and the university have put forward," Grossbach said.
Paul Boni, lawyer for the Woodland Terrace group, declined to comment on the zoning case. Despite the new plan to save the mansion, Boni told the website PlanPhilly, "the underlying legal issues haven't changed."
Matt McClure, lawyer for Penn and Weiss, also declined to comment.
Grossbach said many neighbors want the property redeveloped.
Right now, he said, "it's a blight on the neighborhood."
The mansion has been severely altered: Cinderblock additions went up when it became a nursing home. That happened before 1973, the year it was designated historic.
Aaron Wunsch, a Penn historic-preservation professor, said the house was built when West Philadelphia was becoming a villa suburb in the 1850s. "Levy's house is one of the earliest and largest remnants of that historical moment," Wunsch said.
Wunsch, formerly a critic of Penn's plans to demolish the mansion, called the new plan "a huge improvement."
"One of the things we preach in this program is that preservation isn't about stopping change," he said. "It's about mediating it and doing it wisely."
On Twitter: @ValerieRussDN