NEW YORK (CBSNewYork) – The push to put elevators in every New York City subway station hit a possible roadblock Tuesday.

Several nonprofits organizations and individuals are behind a class action lawsuit calling on the Metropolitan Transportation Authority to add elevators to all stations.

Web Extra: Read The Lawsuit At Center Of Case

“It’s not just for people in wheelchairs. Yes, we’re the most visible ones who need it. But it’s for older people with tired legs, it’s for parents with strollers,” Sasha Blair-Goldensohn, of the Upper West Side, told CBS2’s Jenna DeAngelis. “We filed this suit two years ago, and what’s happened since then? Delay, delay, delay.”

Of the 472 subway stations in the city, the MTA says only 120 are currently equipped with elevators.

MORE: Judge Sides With Disabled Riders, Orders MTA To Install Elevators At Stations Undergoing Renovations

A federal judge ruled back in March the agency must comply with regulations under the Americans with Disabilities Act and install elevators in all subway stations under renovation.

“We saw what happened with Malaysia Goodson – she died doing this,” said Christine Serdjenian-Yearwood, founder of Up-Stand. “It’s a safety concern and we want it addressed.”

Goodson died after falling down subway station stairs carrying her 1-year-old daughter in a stroller. The medical examiner determined a medical episode contributed to her death, but her family believes an elevators could have saved her.

MORE: Mother’s Deadly Fall Sparks Push For More Subway Elevators

Following the tragedy, the MTA board pledged to install 50 elevators in existing subway stations within the next five years. But advocates want action now.

“I challenge all of the MTA board members to spend a week or two on a wheelchair, with a walker and with a cane,” resident Alberto Mercado said.

During Tuesday’s hearing on the MTA and city’s motion to dismiss, the judge said he believes there needs to be some action by the agency, but no decision was made.

Both sides will be back in court on June 5 to re-argue the case. The judge wants the issue resolved and hopes to do so then.