The nito (or Nito Ryu) style of kendo is definitely a thing, and it was championed by Musashi himself, so there is a strong heritage there that goes back to at least the 1600s. It typically made use of the samurai's pairing of katana (longsword) and wakizashi (short sword), normally meant for combat in the open and enclosed spaces respectively, by using them simultaneously.

Sword and dagger was the western version of this, and was also a very common style of swordplay in the 16th and 17th Centuries, being especially useful with long rapiers. The daggers were typically 15-24" long, getting close to short swords in their reach. They were used mostly for parrying, but also for attack if the distance shortened inside the reach of the sword.

"Case of rapiers" was a style of swordplay that utilized two rapiers at once. It was significant enough to be mentioned in period texts like Marozzo and DiGrassi, but was uncommon in practice due to the difficulty in mastering it. The rapiers were manufactured so that both fit into the same scabbard - essentially the sword would split into two separate weapons when it was drawn.

The dagger or short sword was a common sidearm from medieval times, and was generally used as a final fallback weapon when other weapons were spent or broken, or the fight had closed to the point of grappling. Mounted fighters could kit themselves with multiple weapons, and in addition to their primary lance could carry a long (hand-and-a-half) sword for striking from the saddle, a short sword or falchion for more close-up or dismounted work, and a dagger as a last resort. But they didn't really use these all at once; it was more a case of your horse being strong enough to carry a full armoury of options for you, and you would resort to each in turn as the battle progressed. Similarly, two-handed swordsmen would carry additional swords as back-up weapons (as /u/hborrgg and I recently discussed here), as the longer swords were specialty weapons unsuited to close-quarters situations.