The European Competition Commission hit the tech giant with a bill for €13bn (£10.9bn) last week following a two-year investigation into the company's tax affairs in Ireland.
Both Apple and Ireland have slammed the decision. Ireland announced it had decided to appeal the ruling on Friday, after finance minister Michael Noonan said he disagreed "profoundly" with the verdict, while Apple boss Tim Cook dubbed the decision "total political crap".
Now Ireland's Sunday Business Post has reported the European Commission is looking into around six other tax opinions received in the country in the early 1990s, which could lead to further Apple-style tax bills.
Meanwhile, European Commission President Jean-Claude Juncker has denounced Cook's suggestions that last week's decision had a political motive.
"This is not a decision against the United States of America," Juncker told Reuters' reporters at the G20 summit currently taking place in Hangzhou, China.
And AFP reported him as saying: "We are applying the rules. We are basing our decisions on facts and on the legislation."
Apple is not the only tech multinational to find itself in the European Commission's firing line. The commission is also investigating the dealings of Google, which found itself under the spotlight in the UK earlier this year, when it was revealed it had struck a so-called sweetheart deal with HM Revenue & Customs.
The deal earned Google a hearing in front of the Public Accounts Committee, where it was slammed over claims it took advantage of tax havens to lower its overall bill and used loopholes with names like "double Irish Dutch sandwich".
The European Commission declined to comment.