Thanks for that, Britt. If you don't mind, I'd like to attempt to flesh things out (just a bit) for the guys reading... other than Paul (pgsmith), none are Koryu practitioners, so might not quite understand why you're answering the way you are, and honestly, I feel that Scout (the OP) could benefit from having an understanding of what it is you train in.
As indicated in the link that Britt supplied, Suio Ryu is a Koryu (old school) system of martial arts, with the primary focus being on the usage of the sword, most commonly in Iai (sword drawing). However, similar to many other Koryu systems, it has a number of other aspects, which include a form of grappling in light armour known as Kogusoku (literally "small set [of armour/weapons]"), a term also found in arts such as Araki Ryu, Takenouchi Ryu, Sosuishi Ryu etc, as well as pole-arms, and other methods. Additionally, another Ryu is taught alongside Suio Ryu, which is Fukuhara-ha Masaki Ryu Kusarijutsu, a system of a small number of chain weapons, most notably kusari fundo/manriki gusari and kusari gama. This has been since the art was passed to the 9th Soke (head of the Ryu) of Suio Ryu. There are other branches of Masaki Ryu still in existence.
The methods of Suio Ryu are unique and incredibly well designed, with the Ryu taking a very unusual approach to the design of their kata, one which ensures that there is a high degree of reality in their performance. It is a very well respected Ryu-ha, and for very good reason.
But the thing is, I really don't think it, or anything like it, is what our OP is looking for. From everything I've come across, the OP is looking for an (ideally) unarmed Jujutsu approach... but I'm not sure that he really knows what that is in this sense. The feeling I get is that he's after a more modern approach, more in line with BJJ, but with a focus on self defence (weapon defence etc). What has been asked about, though, are more traditional methods, in the form of X-Kan training, and here Suio Ryu (Koryu) training. And, much though I love Takenouchi Ryu, Himura, it was simply not a viable art to bring up. The only schools for the Ryu outside of Japan are for one of the three branches (Bitchu-den Takeuchi Ryu), and are in Hawaii, Canada, and the UK.
But back to what's really being asked about.
This Ryu is Koryu. And that means something. Before we go too much further with asking about these types of systems, I'd recommend reading the following thread, as well as the articles linked within:
http://www.martialtalk.com/forum/showthread.php/93854-The-purpose-of-the-ryu
Anything else, just ask, and I hope I haven't stepped on your toes, Britt.