Is it valid to fast the first ten days of Dhu al-Hijjah with two intentions: the intention of fasting the first ten days of Dhu al-Hijjah, and the intention of making up some days not fasted in Ramadan?

The scholars differed concerning the ruling on making up missed Ramadan fasts during the first ten days of Dhul-Hijjah. One group holds that it is not disliked, citing the action of Umar ibn al-Khattab, may Allah be pleased with him, and arguing that these are days of worship, so making up fasts during them is not disliked. Another group considers it disliked, based on what was narrated from Ali, may Allah be pleased with him, and because the Prophet, peace be upon him, encouraged utilizing these days for righteous deeds, thus it is preferable to leave them free for voluntary acts of worship to attain their virtue. Scholars also differed on the permissibility of voluntary fasting before making up missed Ramadan fasts.