Could an Iron Duke-class battleship accept a substantial four-inch and Pom-Pom anti-aircraft battery?
Short answerYes; six twin four-inch mounts and slightly fewer 40 mm Pom-Poms would be a workable balance.
NotesThere is no fundamental obstacle to the proposed anti-aircraft refit. Six twin four-inch mounts with somewhat fewer 40 mm Pom-Poms would shift weight and space toward the heavier battery while retaining close-range protection.