WASHINGTON — Michael Jordan, the basketball star, was famous for being able to jump 48 inches into the air, putting the top of his head 10 and a half feet off the ground, well above the basket’s rim.

If the Secret Service has its way, the new security fence around the White House will be about three and a half feet higher than that.

Nearly two years after an armed man climbed over the existing seven-foot fence around 1600 Pennsylvania Avenue and ran through the front door of the White House, the Secret Service is moving aggressively to design and build a taller, stronger security perimeter. Visitors to Washington could soon see a 14-foot barrier ringing the president’s home.

Pressure to move quickly is intense; fence jumping at the White House has become a regular occurrence. Two people jumped the barrier last month, including one who had stolen a woman’s purse and was hoping for a clean getaway. There was a jumper the day after Thanksgiving last year. And in 2014, officers tackled a man who had scaled the fence and run onto the North Lawn.