No you cannot rotate your tires too often as it will do no harm to rotate the tires on the vehicle more often than recommended.
It just requires more work to rotate the tires more often and really it's not needed.
Rotating the tires every 5,000 to 10,000 miles is usually more than enough to help with the even wear of the tires.
It is OK to rotate tires every 10000 miles or every oil change to maximize tire life and even the wear out on the tires.
Some people rotate the vehicles tires every 5,000 miles and some people rotate the tires every 10,000 miles which is usually once per year.
The original tires on a new vehicle or quality replacement tires should last up to 50,000 miles before needing replaced with new ones.
The tires that come new on a vehicle are usually the cheapest tires that the manufacture of the vehicle can put on the vehicle.
So some people have the tires replaced sooner after buying the new car because they want better quality tires with a better ride.
But you should easily get 50,000 miles out of the original set of tires on a new vehicle before they wear down and need replaced.
If you drive 10,000 miles per year then that would average out to 5 years before you need new tires.
If you drive 20,000 miles per year then it would be 2 and 1/2 years before new tires will be needed.
Some people drive more miles than other people and need new tires sooner.