Yes, I agree with Peachey. If you just say "Give me a bigger discount." it is very rude. You can say "Can you take a little more off?" instead. So if you are buying furniture and there is a sale, a couch that was $1,000 is not $800 you can say "Can you take a little more off?" to ask for the price to be lowered a little bit, to maybe $700 or $750.

I think the translation includes being appropriately indirect. If you speak too directly in English, you might come across as rude and pushy.

It can be for any situation where something is already off and you want more off. It could be a discount because the cost is already smaller than the original price. It could also be used when getting a haircut after you have already had some hair cut off.