Is it permissible to increase the obligatory maintenance (nafaqah) that a father pays to his son if the current maintenance is insufficient, given that the father is well-off?

There is no blame upon you for filing a lawsuit to increase the maintenance from your father, as long as there are no Sharia courts in your country, and as long as the ruling does not appear to you to violate the Sharia, then you may act upon it. You must fear Allah and be dutiful to your parents. It is not permissible for you to cut ties with him or to mistreat him.