The EPA on Monday added to Volkswagen's woes by accusing the company of cheating on emissions tests for larger diesel vehicles, including luxury lines Audi and Porsche. 

The new allegations resulted in VW being cited by the federal agency a second time.  

The Environmental Protection Agency said the German automaker installed software designed to defeat emissions tests on 2014 to 2016 vehicles with three-liter six-cylinder diesel engines. Volkswagen previously acknowledged rigging emissions tests for four-cylinder diesel engines on 11 million cars worldwide, including almost 500,000 in the U.S. 

The new violations cover about 10,000 vehicles, including the 2014 Touareg, 2015 Porsche Cayenne and the 2016 Audi A6 Quattro, A7 Quattro, A8 and Q5. 

"VW has once again failed its obligation to comply with the law that protects clean air for all Americans," Cynthia Giles, with the Office for EPA's Enforcement and Compliance Assurance, said in a statement. 

"All companies should be playing by the same rules. EPA, with our state, and federal partners, will continue to investigate these serious matters, to secure the benefits of the Clean Air Act, ensure a level playing field for responsible businesses, and to ensure consumers get the environmental performance they expect." 

The agency says the VW software has a timer that makes the cars perform differently when being tested than they perform on the road. While on the road the cars give off up to nine times more nitrogen oxide pollution than allowed by EPA standards, the agency said. 

As before, the EPA said VW may be "liable for civil penalties." The company will have an opportunity to respond to the allegations. Volkswagen faces fines of up to $37,500 per vehicle, which means up to $375 million could be added to penalties already projected in the billions of dollars. 

The EPA said that despite the alleged violations, they do not represent a safety hazard for owners and drivers, and the vehicles "remain legal to drive and resell." 

More information from the EPA can be found here

The Associated Press contributed to this report.