He was a staunch Roman Catholic and an advocate for The Graces, the programme of religious concessions promised by the English Crown in the 1620s, but never implemented.
As a result, he clashed with the Lord Lieutenant of Ireland, the formidable Thomas Wentworth, 1st Earl of Strafford, who was determined to reject the Graces.
Plunket married secondly Susannah, daughter of Edward Brabazon, 1st Baron Ardee and Mary Smythe.
Plunket married thirdly Eleanor, daughter of Dudley Bagenal and Mabel FitzGerald, and widow of Sir Thomas Colclough of Tintern Abbey, County Wexford.
He married fourthly Margaret, daughter of Nicholas St Lawrence, 9th Baron Howth and his second wife Mary White, and widow of Jenico Preston, 5th Viscount Gormanston.