In 1994-95, a quadrangular series was played with Australia, Australia A, England and Zimbabwe as the 4 teams. It was as farcical as it sounds. More of muscle flexing from Aussies showing their might. And surprisingly Eng and Zim agreed to play along https://bleacherreport.com/articles/2321109-world-series-cup-199495-when-two-australia-teams-were-better-than-one

A farce like that where some games of a quadrangular series (where Aus A was involved) were List A matches and others were international matches will never repeat. They even swapped players between Aus and Aus A mid tournament!

The ongoing Test series is closest thing we will ever see to an A team competing with a senior team in a full fledged international series. And on the evidence of India's performance, they are now the powerhouses of cricket similar to how Australia were through 90s and 2000s.