From everything I have heard and seen, once you are at, variously, a 32 or 34, you are pretty much done; there is no benefit to retaking the ACT for college admissions competitiveness. The admissions department will use the score to check that you will keep up if you are admitted; then moves on to the rest of your application to decide if you are a good fit. 32, or 34 (depending on your beliefs), certainly accomplishes that goal.
Here is a twist: For applying to competitive scholarships, where the awarding panel may be much less sophisticated than the admissions department of a university, is it worth it to re-take?
That is, is it likely that if a school gives out 10 (or fewer) of a certain class of competitive scholarship, they will give a higher ranking/score to a 36 than to a 34?
I could certainly envision a scheme where an applicant is given 3 numerical scores: one for GPA + Test Scores; one for Essays; and one for Interview which are then added together for a final score and the top 10 get the nod. In this case, shooting for a higher composite score may make all the difference.
FWIW, I think this is not an informed way to make this sort of selection, but I could certainly believe it if someone told me it is how they do it.
Any thoughts or opinions?
More importantly, any actual insight or experience?
It would be first with scores and GPA. And then they would look at your EC. Most schools only offer merit scholarships to the top few percent of students. If your score/GPA are not at least higher than than the 75%, your chance is very slim to none.
The scholarships which are uber competitive are almost always holistic, meaning that once your scores are good enough they move on to consider other things. A student with a 28 could still get one if his/her essays/EC’s/special circumstances impress the committee. Anything from 25-36 is possible.
Then there’s that in-between category: where selection is based on stats, but it’s not automatic. You’re competing against the rest of the applicant pool, and the school has stated that they’ll only award the top applicants (in an academic sense). You want to aim for 32+ here.
For automatic scholarships (those given to anyone who has the stats), I have yet to see an ACT requirement higher than 34. Different schools have requirements from 21-34 for merit awards of varying amounts. For full tuition or a full ride, I’ve seen requirements range from 27-34, depending on the college, so a 34 should be fine.
So @billcsho, @Lilliana330, it sounds like you think most scholarships are threshold-based: first the committee determines of you are within the pool of contenders with your scores/gpa. Second, they evaluate those in the pool using subjective measures.
Any other opinions? Any insights?
Look up the criteria under scholarships for the schools that you are interested in attending. Some are straight forward and state that you have to be ranked 1, 2, or within the top 5 percent of the class. Others will tell you the gpa cutoff.
What are you looking for: for example, if you are looking for full tuition, then you need to be at the op of the applicant pool because so few of them are being given.
It varies by college. Some with published criteria go above 34 ACT, for example Utah State.
@sybbie719, yes, for full tuition, for example. Or, more insidiously, for an extramural scholarship where the reviewers may be less familiar with error bars at the higher scores. For a 34 one-and-done, where the student is “done” for any college applications; should they try to improve the score for scholarship applications?
What is the “top of the applicant pool”? For an admissions committee, they would likely consider all 32-36 (or 34-36) scoring applicants as being equal.
For a scholarship, will they consider the 36-scorers to be the top-of-the-top; the 35s to be nearly-the-top, the 34s to be nearly-nearly-the-top, etc.; effectively stacking from high-to-low in a monotonically descending hierarchical sort? Or will it be more of a thresholded pool of applicants?
Should the student re-take the ACT in order to be more competitive for scholarships, even knowing that they are “done” w.r.t. college applications?
“For a scholarship, will they consider the 36-scorers to be the top-of-the-top; the 35s to be nearly-the-top, the 34s to be nearly-nearly-the-top, etc.; effectively stacking from high-to-low in a monotonically descending hierarchical sort? Or will it be more of a thresholded pool of applicants?”
OP, what we’re trying to explain is that it’s going to be different for each scholarship. Yes, any of those criteria can be used. It’s up to each college or organization to decide how they’ll evaluate your app for their scholarship.
For the large majority of cases, though, there’s no reason to retake a 34. 
It really depends on the school you are looking at and how likely you can get a higher score. For many top state flagships, 35 is likely the threhold for major scholarships. I know someone even retook for 36 after getting 35 in order to get the presidential scholarship a few years ago.
It depends on the school. I sent you a PM.