Animal-welfare advocates are courting a new Wall Street ally as they take on big U.S. meatpackers: proxy advisory firms.

Groups such as the Humane Society of the U.S. for years have sought to build support among large companies’ shareholders to push for changes in animal treatment, often finding little traction. Now, some pitches are being tailored to win backing from increasingly influential firms that advise investors on how to vote their shares, including Institutional Shareholder Services Inc. and Glass, Lewis & Co.

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