Rashi, Aggadic midrash
Rashi's governing principle is that Scripture never loses its plain sense (peshuto), even though the words of Torah admit of many midrashic readings. He will cite Aggadic midrash when it illuminates a difficulty, but he explicitly distances his own enterprise from midrash-collection: his stated aim is the plain sense, and midrashic expansions are presented as 'our Rabbis of blessed memory expounded,' a distinct voice from his own resolution of the verse.
In Genesis 33:20:1, after giving his own peshat explanation of the altar's name, Rashi reports the Rabbis' midrashic reading that reverses subject and object ('the God of Israel called him El'), and then generalizes: Torah's words can be split like a hammer on rock into many meanings, 'And in reference to all these different explanations it may be said that the words of the Torah... may be given many different explanations.' Yet he closes by subordinating all of this to his own program: 'I however make it my aim to give the plain sense of Scripture.' This shows the method in action elsewhere in the retrieved set as well -- in Ecclesiastes 8:10:2, Leviticus 25:30:2, and Ruth 2:1:1, he brings Aggadah ('Our Rabbis of blessed memory expounded it') precisely where the plain text contains a difficulty (a seeming redundancy, a grammatical irregularity, an unnamed kinsman), using midrash as a secondary resource after grammar and context, never as a replacement for peshat.
The question as posed ('Rashi, Aggadic midrash') is very general; the retrieved passages do not constitute a systematic statement of when Rashi includes versus excludes Aggadah beyond what is shown case by case. The fullest explicit methodological statement among the retrieved texts is in Genesis 33:20:1; the other passages illustrate practice rather than articulate theory.
Among the retrieved passages, only one speaks to the relationship between Rashi and 'Aggadic midrash' as such — the bibliographic note on Midrash Aggadah. It reports that the Maharal held that this Midrash 'was arranged from a single order that had already seen Rashi's commentary on the Torah,' and that it was named 'Midrash Aggadah' precisely because 'many things that Rashi brings in his commentary on the Torah in the name of "Midrash Aggadah" are found in this Midrash.' Yet the note also preserves an alternative possibility: that Rashi and this collection are not in a simple derivative relationship at all, but that 'both of them took these aggadot from a common source that predates them.'
The method here is not homiletical exposition of a verse but transmission of the textual history as given. Following the principle that 'multiple readings can stand together without one refuting the others,' the passage itself offers two accounts — dependence on Rashi, or shared ancestry in an older common source — and does not adjudicate between them. The other retrieved passages (Shemot Rabbah 1:33, 1:34, 10:6, 12:2, 46:2) are classical aggadic expositions themselves, examples of the genre, but they do not discuss Rashi or his use of 'Midrash Aggadah' as a named source; they cannot be enlisted to answer a question about textual lineage.
This passage is a modern editorial/bibliographic note about manuscript history, not itself a midrashic exposition of Scripture; it tells us how later scholarship (R. Shalom Buber, the Maharal) understood the textual relationship, but it does not settle the question with the certainty of a halakhic or exegetical ruling, and it explicitly leaves the matter open ('it's possible'). None of the other retrieved passages touch this question at all, so the tradition's broader view on 'Rashi and Aggadic midrash' generally cannot be drawn from what is given here.
The question 'Rashi, Aggadic midrash' turns out to name two different inquiries that only partly meet. Rashi's own commentary addresses how a peshat-oriented exegete uses Aggadah as a resource subordinate to plain sense. The Aggadic midrash material (as retrieved) addresses a separate historical-bibliographic question: the textual lineage between Rashi's citations of 'Midrash Aggadah' and the compiled work by that name. These are not competing answers to one question but two distinct questions that happen to share vocabulary.