Stada said the buyout firms had sweetened their takeover offer by 25 cents per share to 66.25 euros after their previous 5.3 billion-euro ($6 billion) bid fell through. The revised offer is approximately 16 million euros above the prior offer.
The private equity groups will also lower their acceptance threshold to 63 percent, Stada said, after the last offer failed to win the backing of the 67.5 percent they had targeted.
The new offer is the latest twist for the takeover of one of the last remaining independent generic drugmakers in Europe.
Shares in Stada, which has seen management upheaval and previous failed offers, were up 1.2 percent at 65.27 euros by 1253 GMT, outperforming the German mid-cap index .MDAXI.
Stada's chief executive and its head of finance resigned last week after the failure of the earlier bid.
Stada said Germany's Federal Financial Supervisory Authority (BaFin) had approved the renewed offer, waiving Bain and Cinven from a one-year ban from resubmitting a revised offer.
Carl Ferdinand Oetker, Chairman of Stada's Supervisory Board said it backed the new offer as "a stable basis for developing Stada in the best interest of the company for the future".
Some shareholders including U.S. hedge fund Elliott have bought stakes, speculating on securing a higher price for any remaining stock. The last takeover offer only won the backing of 65.52 percent of shareholders.
Many buyout firms have been flush with cash after recent rounds of divestments and amid cheap borrowing costs.
Sources have said that Bain and Cinven would look into buying more healthcare businesses to combine with Stada over the medium term, seeking cost cuts that would make the high investment in Stada worthwhile.
(Editing by Georgina Prodhan and Alexander Smith)