Is it permissible to say two supplications in the bowing (rukuʿ) or prostration (sujud) during prayer?

The Prophet, peace and blessings be upon him, used to say in his bowing (ruku') and prostration (sujud): "Glorified be You, O Allah, our Lord, and with Your praise. O Allah, forgive me." This does not contradict the Hadith: "As for bowing, glorify the Lord in it, and as for prostration, strive in supplication," because glorifying the Lord in bowing does not preclude supplication, and supplication takes the greater share in prostration because a servant is closest to his Lord when he is prostrating.