Is it possible to raise stats?

You could do that with cheats - either with console command AttributeScore player <attribute> <amount> or there are CheatEngine tables that allow you to do that without loosing Steam achievements.

Custom enchanting will allow you to increase whichever stat you need with your favourite equipment options.

Drugs can do a temporary increase to get through the conversations you want.

That said I know of no permanent way within the game to increase it, neither by level-up nor quest reward.

There are some very specific quests that allow you to increase an attribute, but they require you to be playing an evil and cruel character. These options will generally only appear if your "Cruel" demeanor is high enough.