SAN FRANCISCO — A shareholder rebellion against Dell’s proposed $24.4 billion sale to its founder and other investors is gaining support, fueling a belief that the struggling personal computer maker will have to wrangle a higher price to get the deal done.

Mutual fund firm T. Rowe Price joined the opposition Tuesday. It and another shareholder, Southeastern Asset Management, say founder and chief executive Michael Dell and the investment firm Silver Lake are being allowed to seize control and end Dell Inc.’s 25-year history as a publicly held company for too little money.