I would love to be tattooed by different artists, but like others have said, I would go back to one artist if I were to have one big cohesive piece like a back piece for example. That said, now that I have my crane tattoo by Gakkin on my calf, I am tempted to leave that rest of the calf space for him to add to should I ever go back to travel in Japan again.
On an unrelated note, I remember seeing one guy who just had a eagle chest tattoo done on him the first time I went to Harizanmai. He was only in Kyoto for 2 or 3 days, and then he was flying to somewhere in Europe I believe, to get another tattoo, kind of like a "round-the-world"
tattoo tour. Kudos to him to be able to do it, but it sounds like some rough travelling considering it's all fresh tattoos.