Marriott International sweetened its bid for Starwood Hotels and Resorts Worldwide with more cash, greater synergies and a higher breakup fee. That still may not be enough to deter the Anbang Insurance Group of China and its co-investors from making a counteroffer — yet again.

Anbang, with the New York private equity firm J. C. Flowers and the China-based Primavera Capital, swooped in with a bid for Starwood last week, as the hotel operator was finishing the deal it signed with Marriott in November. That set Marriott in motion, with a new offer disclosed on Monday.

“The proposal we signed last night is not as good for us as the deal we signed and announced in November,” said Arne Sorenson, president and chief executive of Marriott, in an interview with CNBC on Monday. “The deal we got in November, in retrospect, maybe was just too good a deal.”

Starwood deemed Marriott’s new proposal as superior to the one brought last week by a consortium led by Anbang. Shareholders would receive $21 a share in cash and 0.80 share of Marriott for each share of Starwood, valuing Starwood at $79.53 a share, or $13.6 billion, as of the market close on Friday.