The British software firm said it has now been offered £102.7m, up from the £89.5m price offered last month.
The 110p per share offer – formerly 96p per share – represents a 44.7 per cent premium to the stock’s closing price before the offer was announced, the company said.
It is also a premium of 3.8 per cent over the 106p per share bid tabled by Kestrel Bidco, under parent company Symphony, on 12 June.
At the time, Kewill said it intends to recommend unanimously that its shareholders vote in favour of the Kestrel offer, but it yesterday backed Kinetic’s bid.
Kinetic said it also had the support of 25 per cent of Kewill’s stockholders.
London-listed Kewell’s shares jumped 3.9 per cent to 113p.