Comments are complicated here... we do things a bit differently than some sites as far as comments because we get so many of them and our Q&A can quickly get bogged down in comment noise. We try to stay pretty strict to the official comment purposes. The helper text for comments on answers is:

The first thing I recommend is that you stop thinking of the Q&A as "discussions". They're questions and suggested answers/solutions. Discussion is not really part of what this site is for.
If it's a minor suggestion for improvement you can make it a comment or suggest an edit (or make an edit if you have sufficient reputation) but if it's more than that, write your own answer.
Minor additions
If you have one minor point to add, you can absolutely make a comment that is a suggestion for improvement.
So, comments like
- One other point you might add is _____. {brief explanation why}
- Here's an article that supports this suggestion. {link to article}.
- This seems to miss part of the question - {quote from question} - how would you address this?
Not an exhaustive list, merely examples.
Suggestion 1 is a specific detail that adds information and increases the depth of the answer. This is great - hopefully the OP will edit their post to add it.
Suggestion 2 is supporting documentation. This is also really valuable and should be a comment that the OP should consider including.
Suggestion 3 is an example of how you could point out that part of the question hasn't been adequately addressed. One could also consider this a form of "asking for more information" but it meets both purposes to a degree.
Technically, you can actually submit these as edit suggestions... that's what edits are for but it's easier to do on technical, purely objective sites than on sites like ours where answers can involve a lot of personal experience and ... ownership. As such, it'd probably be easier to submit an edit that sources something in the answer (such as suggestion 2 above) - a link to an article with a brief excerpt that corroborates it.
If you do submit an edit suggestion, you should endeavor to explain it well in the edit summary.
But be wary... not everything you might think of as a "suggestion of improvement" will pass for one here.
I'd do ____ instead of ____ but otherwise I agree.
This is an opening for an argument, not a suggestion for improvement. If you want to change something already in the answer, write your own instead.
If you think something is wrong in an answer, ask directly... this is explained in more depth in my answer to this related question about comments (which recommends a comment more like example 3 above).
Again, this isn't exhaustive, just a couple of examples.
Bigger additions
As with points that disagree with an existing answer, if you have bigger additions to an existing answer, you're better off writing an entire new answer of your own. We don't require that answers here be completely comprehensive of the entire realm of possible solutions, but you should still make sure your answer stands on its own. If the other answer gets deleted for some reason, your answer would then suffer for it, so avoid saying things like
I completely agree with the answer from ____ but I'd add {points 1 through n}.
We need to know your full answer, with some sort of support - either personal experience or a good explanation of why your solution is a good one, or some sort of documentation (a study, article, scientific finding, etc).
Because you brought up that PSA, let's look at the question there, particularly the summary:
The real situation in which I'd advocate deleting duplicate answers is when someone comes along later - I'd say at any point later than two hours after the original answer was posted, but that's hardly a hard decision - and posts an answer that has the same method, and the same result, and does not include anything that is not in the first answer.
Having multiple viewpoints on a situation is great. But we don't need a bunch of answers all having the exact same advice stated in a couple differing wordings of the answer text.
Now, real duplicate answers are rather rare. But before starting to write an answer, check to make sure that you're actually adding new information to the post.
It sounds like you're adding new information to the post, so the PSA doesn't really apply in your question.