Depends if Top 20 or not. Many Top 20 schools take very few applicants in R3/R4 as they are also managing waitlists from R1/R2. It is hard to tell for your specific schools.
It is possible to get in in R3/R4 but chances do not depend on you as much as in R1/R2. If you the school has already admitted 22 people with the same background as yours, they would rather take someone else who has less impressive stats for the sake of diversity (it is annoying but often true). If you have a unique profile with a unique value/story then this limitation goes away and you are only up against a fair evaluation. With the application numbers down the last few years, you may have a better chance of not having a very crowded class already.
You won't know until you apply but you do have better chances earlier. The bottom line is
- if R3/R4 is the only time you can apply, then go for it. You can always reapply in the fall (in 6 months).
- if you can apply in R2 but with a weaker application then don't
- Get some free advice from Admissions consultants and be specific with Schools. Don't be vague as you will get vague answers.
Many schools will specifically call out the last round of applications for the international students and usually that's one round before the last one (e.g. R3 if a school has 4 rounds or R2 if the school has 3).
The reason is usually the extra visa/work/prep required for the international students and they often are not able to get all paperwork together from the school to make it in time for orientation (which usually starts sometime in August).
There is also the discussion about the scholarship money (it is allocated strategically and usually little left by R3/R4). I applied in R3 and was able to get in and get scholarship money but that was because I have applied before the deadline.
Founder of GMAT Club
Just starting out with GMAT? Start here... | Want to know your GMAT Score? Try GMAT Score Estimator
Need GMAT Book Recommendations? Best GMAT Books
Co-author of the GMAT Club tests