My personal opinion is that there are two options, depending on the situation:
- You could post a separate answer, clearly explaining that this is a more detailed elaboration of the other answer - both to get some feedback to your approach (which helps you to see whether you understood it correctly) and for the benefit of others reading the same answer.
- Adding this to the answer, but mentioning explicitly in comments why you have added this and making clear that you consider this useful, but the OP should simply rollback the edit if they prefer the version without your addition. (Theoretically you could ask first, then edit, then ask again whether the new version looks ok - but by editing right away you save one round of this exchange.) Apart from the comments, make it clear also in the edit summary why you are making the edit.
The first option is suitable only if your post will be long enough to varant a separate answer. (From the description in your question it seems that this is probably not the case here. Still, if this is at least a bit feasible, to me this seems as better option than a larger edit to somebody else's post. So it is a judgement call: How big change does your edit actually make? Could this post be better as a separate answer?) One more benefit of posting is separate answer is that you are the owner of the post - so you have more control over the content of the post.
Let me still stress one thing - the final look of the answer should be the decision of the answerer.1 It is natural to assume that editor acts in good faith and tries to make some improvements. Minor edits (typos, forgotten dollar, some MathJax mistake, updating dead link) should be fairly uncontroversial. But if you want to make a larger edit, it is important to ask whether the answerer agrees with it. In particular, don't to this if the answerer wasn't online for a long time2 and it is unlikely that they will be able to respond to your edit.
From this viewpoint it is a minor advantage to you that all your edits have to be suggested edits (until you gain 2k reputation points) - which means that the answerer can reject the edit by one click in the suggested edit review.3 (For suggested edits, the edit summary is even more important, since you want the reviewers to see why you want to edit the post.)
TL;DR: Yes, this can be done - but only in some cases, so don't overuse it. Always ask whether the OP agrees with the edit. If the edit is long enough to make a separate answer, that might be a better option. In such case, make it clear in your answer that it is your elaboration of the details of another answer.
1A possible exception are community wiki posts, which are intended for collaborative editing by the community. (Although on this site it is sometimes used to avoid getting reputation for the post - contrary to network-wide guidelines.)
2You can check the OPs profile to see when they were last seen on the site.
3The OP has always final word on the suggested edit, even if it has already been approved by other users. See: Could authors overturn recent community review decisions? and the relevant section of How do suggested edits work?