Delta Air Lines is cooking up what may be one of the most appealing flight upgrades yet: one that allows you to bag a commercial flight altogether and board a private jet.

The new upgrade program, targeted at what Delta calls “high-value customers,” will cost $300 to $800, depending on destination. Beginning as soon as this week, passengers who have achieved elite or “medallion” status in Delta’s SkyMiles frequent-flier program will be eligible for the upgrade offers. But officials stress that the initial number of private jet flights will be small and focused mainly at Delta’s East Coast hubs.

“This is truly a groundbreaking new approach from both industry standpoints,” said James Murray, vice president of operations at Delta Private Jets (DPJ). “Nobody else can do what we’re talking about doing.”

Delta’s decision to merge some of its commercial traffic with its 66-aircraft private jet unit shows the airline’s relentless focus on finding new revenue or squeezing more from existing customers, which is why carriers now appear to nickel-and-dime passengers. Corporate travelers, who are less price-conscious because they book travel on their company’s credit card, represent the most attractive business for most large network carriers.

The move reflects the airline industry’s focus on differentiating air travel and showering their most profitable customers with ever-higher levels of perks and amenities.

Initially, only Delta’s top customers — those at the highest “Diamond Medallion” level, which is met when people spend $15,000 at Delta and travel at least 125,000 miles or 140 flight segments per year — were going to be invited to purchase the upgrades. But the company has spent several months tweaking its model and decided to expand the pool of potential customers by opening it to people at the lowest elite tier, those who travel 25,000 miles or 30 segments annually and who spend $3,000.

DPJ has been testing and revising its model in earnest since May. The company had a customer — who later changed his travel plans — booked for a June 12 flight from Atlanta to Cincinnati on an eight-passenger Cessna Citation X. The first flight is now expected to occur as early as Wednesday, although company officials said the timing remains uncertain.