There is precedence for that, multi carrier groups afford greater aircraft deployment, faster sortie and multi tasking. You also would not need as many ships to protect them as would 2 separate battle groups.
Example of multi carrier task forces with three or two carriers from the book "The USS John F. Kennedy: in Detail & Scale", page 11:
"At the beginning of the gulf war, KENNEDY, AMERIKA and SARATOGA operated on a six day rotation cycle. Two of the carriers would launch strike aircraft while the third would move to an area in the Red Sea, known as 'Gasoline Alley', for two days to replenish munitions, stores and fuel. This meant that each of the three carriers was on line for four days conducting either a morning or evening flight operations schedule, then off line for two days to replenish. The off line carrier was still tasked with standing anti-air warfare and airborne early warning alerts, but it did not conduct flight operations against targets in Iraq or Kuweit.
When AMERICA moved from the Red Sea to the Persian Gulf on February 7, KENNEDY and SARATOGA then changed to a different six day cycle. For two days of the six, both carriers were on line, then for the next two days one carrier was off line in 'Gasoline Alley'. During the last two days of the six day cycle, the other carrier moved off line to replenish. This meant that during the six day cycle there would be two days when both were on line, two days when only KENNEDY was on line and two days when only SARATOGA was on line."
In WWII, Korea and Vietnam there were similar schedules. And if you look at
, you will remember ...
