He was one of leading candidates as the fifth shogun along with Tsunayoshi TOKUGAWA, Tsunashige's younger brother and the lord of the Tatebayashi Domain in Kozuke Province, when Ietsuna became critically ill in 1680 because Ietsuna had no male child, but because Masatoshi HOTTA strongly recommended Tsunayoshi, who was more closely related to Iemitsu by blood, for the shogun, Tsunatoyo did not take office as shogun.
延宝8年（1680年）、家綱が重態となった際には、家綱に男子がなかったことから綱重の弟に当たる上野国館林藩主・徳川綱吉とともに第5代将軍の有力候補であったが、堀田正俊が家光に血が近い綱吉を強力に将軍に推したため、綱豊の将軍就任はならなかった。