Special counsel Robert Mueller’s office obtained new tax and bank fraud charges against Paul Manafort and Richard Gates on Thursday, adding pressure on the former Trump campaign manager and his longtime deputy, who have been fighting the case.

The new indictment, obtained from a federal grand jury in Virginia, alleges the pair engaged in an extensive scheme to defraud multiple lenders and obtain more than $20 million in loans between 2015 and January 2017, including through doctoring statements to show millions of dollars...