Is it valid to fast the first ten days of Dhu al-Hijjah with the intention of making up for Ramadan [missed fasts], along with the inward intention that if it is not permissible to observe voluntary fasts before making up obligatory ones, then it will be [counted as] making up [the obligatory fasts], and is it necessary to make up [the fasts] now?

It is permissible for someone who owes missed days of Ramadan to observe voluntary fasts, according to the majority of scholars. Making up missed Ramadan fasts during the first ten days of Dhul-Hijjah is valid, and it is hoped that its reward will be greater. However, conditioning the intention for a make-up fast on the impermissibility of voluntary fasting before making up the missed days is not valid, due to the lack of a firm intention, and because the validity of voluntary fasting has already been established. A firm and specific intention for the fast must be made before Fajr.