Yes, albeit very difficult and rare
Cash money solves all problems
In The Ballad of Songbirds and Snakes, we learn of the Plinths - a family who made a fortune siding with the Capitol during the rebellion and were eventually allowed to migrate permanently to the Capitol.
It was not the shield that caught Coriolanus’s attention but Sejanus’s outfit, a soft charcoal gray suit with a blinding white shirt offset by a paisley tie, cut to add flow to his tall, angular frame. The ensemble was stylish, brand-new, and smelling of money. War profiteering, to be exact. Sejanus’s father was a District 2 manufacturer who had sided with the president. He had made such a fortune off munitions that he’d been able to buy his family’s way into a life in the Capitol. The Plinths now enjoyed privileges that the oldest, most powerful families had earned over generations. It was unprecedented that Sejanus, a district-born boy, was a student at the Academy, but his father’s lavish donation had allowed for much of the school’s postwar reconstruction. A Capitol-born citizen would have expected a building to be renamed for them. Sejanus’s father had only requested an education for his son.
But it can't buy you acceptance
Unfortunately, the fact that the Plinths had bought their way into the Capitol, and into the lavish lives of the most established Capitol families, unfortunately caused a lot of displeasure and prejudice against them.
For Coriolanus, the Plinths and their kind were a threat to all he held dear. The newly rich climbers in the Capitol were chipping away at the old order simply by virtue of their presence.
Most Capitol-born members, including Coriolanus Snow, always saw the Plinths as 'district'.
They [Strabo Plinth and Coriolanus] were surprisingly compatible. At times, he almost forgot old Plinth was district. Almost.
This is a theme that carries throughout the story, to a tragic end.