Yes, I've done what you are proposing. My answer assumes you are not running 80+ mpw currently.
Without previous experience in running marathons, and with say a base of 50 mpw, you will not be able to run a second marathon in one week and you will regret running one in two weeks. Your first marathon will be a joyous occasion to you. On the second marathon, within the first 10 miles, you will know that you have at least 16.2 miles to suffer from you decision.
You will eventually be able to run frequent marathons, and enjoy them. For now, though, do the best you can on your first marathon. Keep training afterwards. Determine when you feel like making your first post-marathon long run. This will give you an idea on how frequently you can schedule same-season marathons.
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