I have first-hand experience on this, I applied in R3 then reapplied (& got accepted) in R1
I use the same recommender from R3 to R1, though I made sure they applied much revision to their recommendations
In term of the technicality, you need to ask for the recommender to submit their recommendation again (restart the whole process in R1)
I heard that it will be more difficult for you to get in if you got dinged without interview previously. I redid almost all part of my application, and I also gained a significant experience that boost my profile in R1. So I would highly suggest you to apply in R3 only if you’re 100% sure you have put together a very compelling application. If not, might be better to tell your recommender that you decided to apply in R1 instead and for them to resubmit their recommendation
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