Could a group of modernized older battleships pose a serious threat to Yamato?
Short answerYes; several radar-equipped ships concentrating accurate fire could overwhelm assumptions based on Yamato fighting only one or two opponents.
NotesOld battleships were not harmless simply because their original designs predated Yamato. Fire-support ships could receive radar and improved fire control that made their existing guns more accurate. Yamato might be designed to fight two such opponents, but four or five firing together create a very different damage problem. Armour may stop an initial hit in a protected area, yet repeated impacts can disable systems and strike places already weakened by earlier shells.