Is it permissible to fast the six days of Shawwal along with Mondays and Thursdays with a dual intention, and does the same apply to fasting Ramadan and Mondays?

The issue of combining intentions (tashreek fil-niyyah): if it is in the means or if the acts overlap, then it is valid, and the objective of both acts of worship is achieved. An example is the ritual bath of a person in a state of major ritual impurity (junub) on Friday with the intention of performing the Friday ghusl and removing the state of major ritual impurity. Similarly, if one of the acts of worship is not intended for its own sake, such as the salutation of the mosque (tahiyyat al-masjid) with another obligatory or supererogatory prayer. Therefore, there is no harm in combining the fasting of Monday and Thursday with any other fast, because the desirability of fasting them is due to deeds being raised on those days. However, the questioner should not combine the intention of a supererogatory fast with an obligatory fast.