Would taking more 3-4 weeks in submitting my secondaries be detrimental to my application?

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I think your question hasn't gotten answered because it isn't quite clear what you mean.

Are you asking if waiting another 3-4 weeks to submit your primary application would be detrimental?

If so, I would say no, but you are begging to push the envelope. If you have a physician letter, then you should just apply, and add the DO letter when it comes!
 
I am sorry, I just realized the grammatical mistake that I made in the post heading. Yes, you understood my question right. I received secondary's from school last week. And it will take another 2-3 weeks before I will receive my DO LoR. Although I already have my MD letter uploaded in AACOMAS, I am not sure if I should also wait for that DO letter to give me that extra edge as an applicant or whether taking more that 2 weeks for turning in my secondary's from the date I received them will be detrimental for my applications.
 
Honestly just submit it, and send the letter later. I think there are...3 DO schools that even require a DO letter? For most places, it's just a nice thing to have.
I got my DO letter much later after submission, and I've only sent it to PCOM, because the DO I shadowed was an alum.
 
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