You cannot apply for an extension in you entered under the Visa Waiver Program.
You can only apply for an extension if you entered with a visa stamp.
Unfortunately, I don't make the laws! I would throw open the doors and allow every single brother, sister, married child, single child and spouse into the US without waiting their turn in line like the law requires.
However, I did give you a link to read which thoroughly explains that there are a limited number of visa numbers available for each category and everyone has to get in line.
Even the brothers and sisters of US citizens who are living in all those countries you see on the news with bombs blowing up and killing people on the street have to wait their turn.
There is no option to jump ahead of the line.
Again, don't shoot the messenger. There is no reason for me to not tell you of an available avenue for your brother.