Yeah, you're talking about Shinto Muso Ryu (or Shindo Muso Ryu, both are correct) there, JKS. To fill in the details on Himura's comments, the story told within Shinto Muso Ryu is that the founder, Muso Gonnosuke, was a licenced practitioner of both Katori Shinto Ryu and Kashima Jikishinkage Ryu, and a specialist with the Bo. He met Musashi Miyamoto during his Musha Shugyo (warrior travels), and the two had a friendly duel. You could tell it was friendly, because Muso was alive at the end of it. Despite his skill and experience, Muso Gonnosuke had found that he couldn't get past Musashi's juji-dome (a block using both swords, forming a cross-shape), which Musashi was using to control Muso's Bo, and move past it to a "killing" blow. Disheartened, Muso went away and meditated at a temple, training every day for a thousand days (there are a number of different versions of this, some have different time-frames, some don't have any, but 1,000 is a good symbolic number often chosen for these stories), after which he was resting under a tree. While resting, he heard a voice say to him "Maruki o motte, suigetsu o shire" (With a round stick, know the suigetsu [literally, water on the moon, which is a tactical teaching referring to optical illusions, as well as being the kyusho point of what we refer to as the solar plexus]). With this new insight, Muso developed a new weapon, which he called a Jo (stick, as opposed to Bo, staff). It was differentiated from a Bo by being shorter and thinner, making it a faster, more manoueverable and versatile weapon. Armed with this, and his new methods, Muso went back and saw Musashi for a rematch. This time, when Musashi went for his juji-dome, Muso Gonnosuke was ready, and countered, giving Musashi his only defeat. The technique used is still taught as part of Shinto Muso Ryu today in the higher levels (around Okuden... different lines sometimes change where things are). There are no versions that have Muso Gonnosuke losing the second time, or even being a draw.
Catch is, of course, that this is only part of the oral tradition of Shinto Muso Ryu, and is not supported by any other sources, including the school of Musashi. A corner stone of the legacy of Musashi is actually that he was never beaten, even in friendly duels such as the ones that he is claimed to have engaged in with Muso Gonnosuke. In fact, there isn't any clear evidence that the two even met. That doesn't change the fact that there is a technique designed specifically to combat an opponent with two swords, most notably against Musashi's juji-dome (although it really must be stated that such an action is not exclusive to Musashi's approach, and it turns up in most other systems that use two swords).
Other than that, there are occasional techniques within one or two sword systems that I know of that are designed specifically against other sword systems common traits, or specific attacks... such as a technique within Musashi's system of Hyoho Niten Ichi Ryu which seems to be the technique used to defeat Sasaki Kojiro, who was famous not only for his size, and the length of his sword, but for an incredibly fast attack called Tsubame Gaeshi (Swallow Return), in which the sword is slashed down, then up so fast that the blade blurs, giving the appearance of a swallow's tail.
Then you get groups of methods in some systems to counter possible methods that could be encountered... such as some lines of Yagyu Shinkage Ryu who feature a set of methods called "Nito Yaburi" (two sword breaking), designed to defeat an opponent who is armed with two swords when you only have one. Similarly, schools such as Katori Shinto Ryu focus on single long sword, and each of their other weapons are dominantly taught to prepare the swordsman for handling such an opponent, including naginata, yari, bo, even two swords (which are known as ryoto, meaning "both swords", as opposed to nito, which refers to "two swords", to imply the usage of a long and short, rather than any other combination).
There's more, obviously, but we start getting into proprietary knowledge at that point.
One thing to remember about the idea of "getting as much information as possible about your opponent" is that these systems would be quite closely guarded, in the main, so it wouldn't necessarily be that easy to get an idea of exactly what you might face. That was more a possibility when it was peace-time, and dueling was a real possibility, as schools would then compete for students, and patronage of daimyo, so they would put on demonstrations more frequently... but even then, what was shown was often only a tiny aspect of what really existed, or was altered from the way things were really done in large or small ways. A number of Ryu maintain this tradition to this day, such as Fusen Ryu, Kage Ryu, and a number of others. Then there were arts that were Otomo Ryu (essentially, the "official" school of a particular domain, or lord/daimyo), so, having achieved such patronage, there was less need to advertise, as the local daimyo was sending his samurai to train with you anyway. Shinto Muso Ryu was one such Otomo Ryu, of the Kuroda clan in Fukuoka, so it was rarely seen outside of that Han (area). And when a demonstration was done, it was often only a single kata, Tachi Otoshi, although later a newer, adapted set of kata (not officially, or originally Shinto Muso Ryu), known as Matsumura no Bo would be shown. This set was developed for a young girl in the family of the head at the time, for whom a Jo was about Bo height... not all lines teach these techniques, though.
