STEP UP Meaning of STEP UP in English phr verbStep up is used with these nouns as the object: ↑ campaign , ↑ demand , ↑ effort , ↑ fight , ↑ gear , ↑ hunt , ↑ industrial action , ↑ production , ↑ tempo Oxford Collocations English Dictionary. Оксфордский английский словарь словосочетаний . 2012