Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this Fatwa:
1- As a priority, the first option is to always make the obligatory actions up.
2- The second option is that let’s say you had many fasts to make up, like twenty, and you started on the 10th of Shawwal. So, once you finish the obligatory, you are going to be outside of Shawwal. So when are you going to do the six days of Shawwal? Well, what you would do there is that you would actually do the obligatory fasts, and then you would follow it up with six extra with the intention of it being Shawwal even though you are not in Shawwal.
3- The third option is that if you have many missed fasts, you can begin with the six days of Shawwal and you can make up the missed fasts later.
Sheikh Abu Eesa Niamatullah answers these questions in this Video:
Source: Faith IQ Facebook page.
Allah Almighty knows best.