From Longman Dictionary of Contemporary Englishtake somebody up on something phrasal verbACCEPTto accept an invitation or suggestiontake somebody up on an offer/promise/suggestion etc I’ll take you up on that offer of a drink, if it still stands. → take→ See Verb table
Examples from the Corpus
take up on • You don't take me up on anything - you just repeat it in a different order.• At least six thousand Mennonites took her up on it.• I offered myself up to be corrupted, but nobody took me up on it.• Might take her up on it.• What if I should take you up on it?• Not one took me up on my offer to know more!From Longman Business Dictionarytake somebody up on something phrasal verb [transitive] to accept an offer or invitation that someone has made2000 managers took up the company’s offer of voluntary retirement. → take→ See Verb table 