Engineering firm Melrose increased profits by 57% in the first half of 2011 and said it was working on another offer for rival Charter International.Pre-tax profits after exceptionals at Melrose came in at £63.1m compared to £40.3m the previous year.The firm increased its interim dividend by 15% to 4.6p and said its three continuing divisions performed well during this period, with operating margins ahead of target.Yesterday Charter confirmed speculation that it has received a second offer following one made by Melrose. Christopher Miller, chairman of Melrose, said: "Following the Charter announcement yesterday we have asked Charter to cooperate in a diligence process and to lengthen the "put up or shut up" timetable to assist us in presenting an offer for their shareholders' consideration."