Although Kali and Escrima do bery well at teaching the aspects of knife / blade fighting they do not exclusively train with them. There are many martial arts out there that use the ability to learn how defend against a knife attack but few that focus on fighting knife against knife.
For that type of training I would recommend you get a hold of Jim Wagner or Richard Ryan, both who are experts in close quarters and blade fighting. Their systems include a huge emphasis on knife fighting and they are excellent at teaching them. I took some knife fighting courses when I was in the Army and they pailed in comparison with those two. They hold seminars all over the US and it is definitely worth it to attend them. You should take a friend who has training with you so you have a partner to train with as well.
Another name to remember about knife fighting is Thomas Sipin. He is based out of Wisconsin and is one great instructor. Good luck.