An Engine spokesman said the company was confident that the sale would go ahead and confirmed that a new deadline had been set.
He said: "Lake has extended its offer in order to listen to shareholder concerns and gather further acceptances. We remain confident that we will progress as planned in due course."
The close-to-£100m deal, which PRWeek revealed three weeks ago, is yet to go through amid a stand-off with 72 shareholders who hold a combined 29 per cent of the marketing services group's shares.
Engine needs at least 75 per cent of shareholders to accept Lake's offer for the deal to go ahead, but the deadline set by Lake for acceptances came and went at 5pm on Wednesday.
Lake has set a new deadline, believed to be towards the end of next week. It is not clear whether it plans to improve its offer, but so far it has not done so. It is thought that this is because it does not want former employees, some of whom now work for rival companies, to be shareholders.
Engine declined to say whether dissenting shareholders would be made a better offer ahead of the new deadline.
The dissenters are unhappy with the terms of the current deal as they believe it unfair that they have been offered a lower value per share than current employees, with no option to retain shares in the new company.
One reason for the price differential is because ex-employees have been offered cash for their shares while current employees will be offered shares in the new company.
Lake Capital has so far refused to improve its offer.