All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
According to the majority of scholars, it is impermissible for one to fast in Ramadan along with the intention of any other fast. Hence, if it is impermissible for one to fast in Ramadan along with another intention such as the voluntary fast, the fast of expiation, or making up for missed fasting days (for example, it is impermissible for the traveler who is allowed not to fast, to fast during the month of Ramadan with the intention of expiation, etc.), then combining the intention of fasting in Ramadan and other fasts is even more impermissible.
Consequently, whoever does so, his fast will be invalid and he must make up for it.
Allaah Knows best.