As someone who is an introvert and not very good with having a small talk with strangers, I usually just make it simple without asking: a minimum of 3 acceptable photos, let them review, then take more if they request (provided you have the free time to fulfill their request).
Almost always, when someone asks me to take a photo, I will straight up agree and take a position. For each take, I'll just make it short by initiating a countdown (or count-up in this case)
1... 2... and.... 3! ... once more!
Each take won't take more than 10 seconds, and I do this until I get 3 acceptable photos. ("Acceptable" in this context means "not photographer's fault", like blur due to shaky hands, lens blocked by the photographer's hand and passing travelers, etc.)
After this, then I'll let them review the photos by saying,
Are these okay?
More often than not, they will find them okay, thank me, then move on. Sometimes they'll request more, sometimes with additional instructions, and I'll do the same approach again as long as I have the time. Otherwise, I'll reject the request politely.
Sorry, I have something to catch.
An exception is if when they are in hurry while I try to get the first 3 acceptable photos, then they'll interrupt me. Still, they'll usually thank me because it's better to have something than nothing. But usually, people are always happy to have more photos, as long as you're okay with it.
I'll consider to "just go with the flow": take more if they request, stop if they feel enough.
Something to ponder from the requester's perspective is that:
- They're entrusting their personal belonging (sometimes not a cheap one!) to a stranger.
- Not everyone is a skilled photographer.
So, more often than not, they will always feel grateful to have at least 1 okay-ish photo and most importantly, getting their personal belonging back!