I’ve done back to back drains (maybe 10 miles in between each) before without much harm on transmissions of vehicles that I know history of. Knowing what I know now, I’d probably space out the drains and put some miles in between. This is to allow new atf fluid, which is an excellent cleaner, to clean up and pick up debris if any, and then flush it down the drain. Doing it 3-4 times as you’re intending, would allow the maximum amount of debris to be flushed out with a simple drain and refill each time, while allowing new fluid to use its cleaning ability in between each drain and pick up debris. I’d do several thousand miles in between each which comes out to one drain, every two months for the average driver.
I may have missed it, but what type of vehicle, miles, transmission service history and the type of fluid are your planning on using?