I have read in George Imirie webs that you have to add a super with foundation, if they were supers with drawn comb you would be able to add three at time.
The bees will draw the foundation if they find nectar sources. If you feed you will see how fast they work.

I would read to George Imirie. Vamos, que lo voy a releer. I am going to re-read him.

My colony has 2 brood boxes with 2 small supers on top. The lower super is about 2/3rds full. They have yet to draw comb on the top one.

This hive is about a year old and was started from a single swarm cluster that happened to land in my back yard.

As the colony had to start from scratch, so to speak, I can't comment on how fast it would take a full hive to fill 3 supers, but feel that 2 probably would be sufficient.

You will probably be inspecting the hive from time to time, and if it looks as if they are able to fill out the supers faster, then more could be added then.

In my opinion, if supers are added too fast, the bees won't be able to keep up anyway. When the top super looks about half full of honey, then I would add another at that time.

Bejay