On Jan. 19, Milestone had agreed to be bought out by Starwood for $16.15 per Milestone unit in an all-cash transaction.

Starwood on Wednesday raised its offer to $16.25 per Milestone unit, representing a 2.1 percent premium to Milestone's Tuesday closing price of C$21.30, according to Reuters calculations.

ISS said in February that the initial deal terms had prioritized "speed and certainty" over price.

In contrast, Glass Lewis had encouraged Milestone unitholders to vote for the buyout.

Institutional unitholders, who make up 16 percent of Milestone's voting units, will vote in favor of the new offer, Milestone said.

Reuters reported last month that Milestone was in talks with Starwood for a higher offer price.

Barry Sternlicht-led Starwood Capital manages about $52 billion in assets and focuses on real estate.

Dallas-based Milestone, which went public in Toronto in 2013, owns and manages apartment properties targeting blue-collar workers across the U.S. Southeast and Southwest.

(Reporting by Ahmed Farhatha in Bengaluru; Editing by Sai Sachin Ravikumar)