From Longman Dictionary of Contemporary Englishstep up phrasal verb1 INCREASE IN ACTIVITY, FEELINGS ETC step something ↔ up to increase the amount of an activity or the speed of a process in order to improve a situation The health department is stepping up efforts to reduce teenage smoking. stepped-up security at airports2 (also step up to the plate) especially American English to agree to help someone or to be responsible for doing something Residents will have to step up if they want to rid this area of crime. → step→ See Verb table
Examples from the Corpus
step up• Her ankles can not handle the slope, and so she turns around, walking backward, tiny three-inch steps.• I stepped right up and gestured in the rain; they consulted.• A flight of steps leads up from the courtyard and there is entry also from the house end.• A flight of steps goes up the left-hand side of the gallery.• It was the first important step in breaking up the pack.• Both moves were seen as tentative steps towards opening up the political system.• They are sitting on the wooden steps that lead up to the front porch of their house.• The steps leading up to the launch of a new product or product line are just as numerous.From Longman Business Dictionarystep something → up phrasal verb [transitive] to increase the amount of an activity or the speed of a process in order to improve a situationWe will be stepping up production to meet increased demand. → step→ See Verb table 