As it stands, martial arts in storyteller are a bit of a nonissue - they are character background only, and make no fundamental difference to the system - its still "I hit/dodge/disembowl".
A proposed alteration is to use additional skills/talents for a martial art, and that each of these skills has its own set of special maneuvers, like Brawl in the core rules. Each martial art might have its own dodge, brawl and melee skill, each with its own maneuvers.
For example: Frank decides his character is a student of the martial art MArt. MArt's style is one of quick and adaptable moves rather than of heavy decisive blows, and it doesn't rely on weapons as all. Frank and the ST have a chat about what sort of manuevers and such and work out something they are both happy with.
Frank decides to take 2 points in Dodge and 2 points in Brawl, in addition to his 2 points in MArtDodge and 3 points in MArtBrawl - he decides that his character learnt to punch on first, before learning MArt. He takes Evasive Action and Taunt as his brawl special manuevers. He then starts to think about special maneuvers for the martial art.
Example: Frank decides that MArt would allow an observant person to get an advantage over an opponent if they first see them fight. He suggests to the ST a special maneuver of that type for MArtBrawl and they work out mechanics for it.
If Furter does not take any action against an opponent (other than dodging) for a turn, at the start of the next turn, Frank can roll Per+MArtBrawl at difficulty 7. For each 2 sucesses, Frank gets a -1 difficulty to dodging or attacking (using MArtBrawl) against that opponent. This benefit usually lasts for the scene, but if the opponent is sufficiently experienced (3 in brawl/dodge/etc) or knows multiple arts, they can realise what is happening and try and change their style, removing the lowered difficulty.
For instance, Frank's character (let's call him Furter) is fighting against an opponent (call him Oppy). Furter drops back and watches closely as Oppy strikes at him. At the end of that turn (not tick, one whole turn), Frank rolls Per+MArtBrawl. He only gets 2 sucesses, giving him a -1 to strike or dodge when rolling Dex+MArtBrawl for the rest of the combat, Oppy being just a thug and not well trained.
Frank considers another MArtBrawl speciality, and suggests that the Art was developed by those with no weapons against those with weapons, so a disarming sort of maneuver seems appropriate. The ST agrees, and they decide that a Dex+MArtBrawl roll and then a Strength + [succ] roll vs 6, needing the opponent's Strength worth of sucesses to lever the weapon away seems appropriate.
After talking some more with the ST, Frank takes a maneuver they call Double Up - the character has learnt to dodge a blow with such adeptness that he can follow up a dodge with a strike. The maneuver needs to be bought for both MArtDodge and MArtBrawl. In game terms, the player declares a dodge and rolls Dex + MArtDodge. For every spare sucess above what was necessary to dodge, they can then roll that many dice to strike back in the same tick (limited by their Dex + MArt). This does not use up one of the character's existing actions.
Fighting Oppy again, Oppy strikes at Furter, and Furter dodges, calling on his knowledge of MArt to avoid the blow. Oppy's player rolls Dex+Brawl and gets 2 sucesses, Frank rolls Dex+MArtDodge and gets 4. Frank therefore has two dice to strike back at Oppy after sucessfully dodging. Franks rolls them bones, as Furter strikes back at Oppy after avoiding the initial blow. A sucess, so Frank rolls for Furter's damage.
Different maneuvers could be developed for a given style of art. This isn't intended to overcrowd the system, but more to provide for those folks who want to have learnt to have beat people up in a particular way. Not all of the maneuvers need to be actual combat maneuvers either - see above for an example of an alternative maneuver.
The maneuvers should allow a character to accomplish a task at a slightly lower difficulty that they would be assigned without the maneuver: if something would be difficulty 8 then a maneuver might allow a character to accomplish it at difficulty 7 or maybe even 6.