The board of HR Owen accepted a new £43.2 million offer from Malaysian tycoon Vincent Tan and has urged shareholders to do the same after he increased his proposal by 31% from an earlier £32.5 million.
HR Owen sells high-end marques including Bentley, Lamborghini and Ferrari from 14 sales franchises mainly in London.
It could now go international after Mr Tan's investment arm Berjaya Philippines said it plans to expand the brand abroad.
Berjaya now owns or controls almost half of the company's shares, and has given investors until September 27 to accept its 170p per share offer.
HR Owen said it weighed up Berjaya's new offer and concluded it represents "fair value" for the company, after rebuffing its first approach as "unacceptable". It recommended shareholders also accept the new offer.
The company's acceptance looks set to end to a two-month hostile takeover tussle, after Berjaya made its first approach in mid-July.
Berjaya increased its stake in HR Owen in June to 29.8% - just below the level where firms are forced to make a takeover bid.
Bentley Motors, which has a 27.9% stake in HR Owen, declined to say whether it will accept the higher offer.
HR Owen was founded by Harold Rolfe Owen in 1932. It also has 17 aftersales franchises.
Mr Tan, one of the world's richest men, owns 45% of Berjaya Corporation, the buyout-firm's parent company.