Is it permissible to fast the day of Ashura with the intention of making up for seven days of fasting from Hajj al-Tamattu'?

It is permissible to combine the intention for a make-up fast and a supererogatory fast, such as 'Ashura. However, it is better to intend each fast separately to receive the full reward. It is also permissible to combine the intention for the 'Ashura fast and the Tamattu' fast, because the Tamattu' fast is an obligatory fast that does not have a specific time, similar to a make-up fast.