Well, I take different breaks depending on how I feel so I can start new 7-minute set either immediately or have some time to recover in between if I feel not so great on that given day.
I basically started with the original set, for two months I tried to increase number of repetitions during each phase without hurting myself, then after I pushed to my peak intensity my body got adapted to it so I added a 2nd set at a lower intensity and was slowly increasing it. The same repeated later and I added 3rd set. Now I can push all 3 sets at the same intensity (actually, 2nd and 3rd are easier), and I tried adding 4th one but got an injury so I decided to stick with 3 as my optimum.
I can't find it in the NYT article so maybe it was in the original paper, but I'm pretty sure the 7-minute workout was always meant to be repeated three times (although maybe not directly after another).