Is there an adjective for people who asks for more than offered?

This idiomatic expression uses a verb phrase instead of an adjective:

I could ask them for another favor, but I don't want to take advantage of them.

or even (in spoken language):

I could ask them for another favor, but I don't want to take advantage.

Take advantage:

To make use of for selfish reasons; achieve a selfish goal by exploiting: took advantage of him by leaving him with the bill; took advantage of his unsuspecting nature.

"I know someone who has helped me a lot some time ago, and I could ask them for other favor, but I don't want to because I don't want to overstep."

For the more specific example of staying for lunch, an applicable term would be "outstay my welcome."

I looked up the Chilean definition, which roughly translates to "Bold or Confident". Other translations colloquially suggest someone with big feet or big eyes, combined this all seems to suggest a specific personality trait being used as an adjective in this negative connotation.

I feel the best adjective match would be the word "imposing", using your usage examples, the sentence structure still fits and conveys the meaning you appear to want.