The Australians started something unique. They had a tri-series at home involving England, and guess who, Australia A. You thus had two Australian teams in the same tournament, and both made the finals, but the way this happened was then questionable, and the international status for the series was withdrawn.
Then came the 1998 Commonwealth games. The Indians sent a team for the event, led by Tendulkar. That happened to coincide with the Sahara Cup, an exhibition series against Pakistan in Toronto. In a rather tight spot, they sent another Indian team for the event. These twin teams, however, were not so successful, as neither won anything.
Today, there's a problem of workload, and teams say there is too much cricket being played. The impact of T20 is also significant, even as we find more and more exhibition tournaments being scheduled. Is there any scope for two teams to play internationals together? It wouldn't hurt to send the main team for proper tours and (more or less) reserve teams with a frontline player or two for those Sahara Cups.