Next at sea from 30 August to 27 September 1944, "Cogswell" sailed in the carrier screen as strikes were hurled at targets in the Palaus and Philippines during the invasion of Peleliu. On 6 October, she sailed from Ulithi for the air strikes on Okinawa and Formosa in preparation for the Leyte landings, and fired protective antiaircraft cover for her force during the Formosa air battle of 12–14 October. After guarding the retirement toward safety of and , she rejoined her force for air strikes on Luzon and the Visayans, and screened them during the Battle of Surigao Strait, one phase of the decisive Battle of Leyte Gulf. She returned to Ulithi on 30 October, where future astronaut Alan Shepard joined the ship as a gunnery officer, but put to sea 2 days later to return to the Philippines. After was damaged by a submarine's torpedo, "Cogswell" guarded her passage to the safety of Ulithi, then returned to screen air strikes on Luzon, the landings on Mindoro, and the air attacks on Formosa and the China coast which neutralized Japanese bases in preparation for and during the Lingayen invasion. "Cogswell" screened , hit during an air attack, into Ulithi 24 January 1945, and sailed on to the west coast for overhaul.