What are the days when one can fast with two intentions in a single day?

We do not know of any fast in which the intention can be shared, because it does not overlap and is an end in itself. The reward for voluntary fasting may be attained by one who fasts to make up for missed days or to fulfill a vow on days when fasting is sunnah (definition) (such as Mondays, Thursdays, and Ashura), but this reward is not the same as the reward for one who fasts with the sole intention of voluntary fasting.