Hancock said the offer price will increase from A4.2c per share to 4.45c per share if acceptances rise over 87% before the bid closes next Friday.
The company will also pay the additional 0.25c to shareholders who have already accepted.
Hancock's interest in Atlas is currently 76.3%, though Fortescue Metals Group still holds nearly 11.4%.
Hancock CEO Garry Korte said acceptances to date had been pleasing.
"The offer has been unanimously recommended by the Atlas board, and the high level of acceptances to date reinforces that our offer represents a compelling opportunity for Atlas shareholders to realise value from their shares which is in excess of their fair valuation as determined by the independent expert," he said.
An independent expert concluded the offer is fair and reasonable to Atlas shareholders.
Atlas reiterated today that its lenders had chosen not to accelerate the company's repayment obligations, despite its rights to do so due to the change of control.
If lenders accelerate payment of the $85 million debt, Hancock has indicated it would make funding available.
Atlas posted a 2018 financial year loss of $163 million last month.
Shares in Atlas gained 0.1c to 4.3c.