Hi Highwyre,
I don't know to which schools you're applying, but my view is that your scores are solid, and I wouldn't take the GMAT again. As I mentioned earlier, when I was on the adcom, we saw all scores that were submitted to our program (i.e., everytime you checked off the box on which schools should receive your scores, the schools get the scores. They don't magically disappear from your file just because you took the test again).
Here are my specific comments:
(1) A score of 710 is fine. No one will be low-whistling with respect at this score, but no one will be worried about whether or not you can handle the curriculum either. With a score like this, you're right in the mix. Unless all of these points are from qual, and you have no quant background, I wouldn't worry, and I would instead focus on your essays and making the rest of your application as solid as possible.
(2) Right now your scores are on a nice trajectory. You've improved each time. This will indicate you were just getting comfortable with the test, its format, and the pressure of it. But your raw intellect – as indicated by the 710 score – shows you're smart and you can handle the work. If you take the test again and it's lower, it throws you off this trajectory and it makes that 710 look like a fluke.
(3) Three attempts at the GMAT is (kind of) at the upper bound of how many times people take this test and submit the scores to a single school. My own personal observation while on the adcom was that there was very little distribution in terms of the number of times someone took the GMAT. Meaning, most people (90%?) took the test 2 or 3 times, but VERY few took it just once or 3+ times. More than three attempts, and it starts to feel like you're totally focused on just getting a great score rather than understanding what the program is looking for and telling your story.
(4) Unless you have some overall intellectual concerns that I just dont know about (low GPA, no quant background, etc.), then perhaps a higher score would benefit you. But with three scores already submitted, a fourth score – even if it's higher – might not incrementally be of material value.
As you probably inferred, evaluation of a candd's GMAT score is part art and part science. It's never looked at in isolation, and is just one component to the overall story.
I've written (hopefully a helpful!) article on this topic, which you can find here:
https://www.thefirstread.com/how-the-adc ... plication/Hope that's helpful,
-James Young