Alesco went to the High Court but the IRD's position was upheld by Justice Paul Heath in 2011.
Alesco took the case to the Court of Appeal, where it was dismissed in a unanimous decision this year.
Alesco then sought leave to appeal to the Supreme Court, which was granted yesterday.
But tax adviser Daniel Hunt said Alesco's use of OCNs was artificial, lacked commercial reality and was "obviously tax avoidance".
"I think the chance of success at the Supreme Court is virtually impossible," he said.
While the amount in dispute is about $8.6 million of tax, penalties and interest, it is viewed as a test case.