Should I re-take the GRE?

[IAmtheLaw68]

Hey all, just looking for some thoughts/opinions on whether or not I should re-take the GRE. I just graduated and am planning on applying to joint-MBA/MPA-ID programs in about 4 years. I took the GRE twice -- I got 168 V/156 M/5.5 AWA the first time (April 2019) and 167 V/163 M/5.5 AWA the second time (June 2019). My top choices are Harvard and Stanford (HBS/GBS and HKS/GSB). I'm also very interested in certain 3-year DPhil programs at Oxbridge.

I'd mostly like to grind a bit on math for ~8 weeks and then re-take the test in the fall before I start work. How much good would this do to my application? Does re-taking a third time look bad? What are the risks here? I'm also assuming I'm fine not to take the GMAT since I'm applying to joint programs, but if anyone has insight here let me know.

If it's necessary/helpful: I graduated from HYPSM with a 3.72 (post-freshman GPA is 3.87, major GPA is 3.96) in economics, going to MBB post-grad, excellent resumé (successful start-up, publications, good internships, etc.), hoping rec letters will be good/very good but may not be eye-catching or stellar. Female, URM but debating whether to put it in on the app for personal reasons.

Edited June 22, 2020 by IAmtheLaw68