[Concept]
The "Purifier SMG": an accurate, low recoil Amarr SMG. The longer you fire continuously, the more the weapon's rate of fire increases; this means you start with low damage per second, but it gradually increases as you keep firing (similar to the laser rifle). The weapon should also have heat buildup and overheat, and the increasing rate of fire should make the heat buildup and overheat happen faster; this means burst firing to reset the rate of fire to its initial level is a good strategy to avoid overheating, but also means you have to sacrifice the DPS-gain. The increasing rate of fire from continuous fire should also severely decrease the weapon's accuracy.

Here is a video of a weapon with a similar mechanic to get a better idea of what I am proposing.

[Stats (standard)]

Damage profile: laser (+20% damage to shields, -20% damage to armor)

Range (optimal/effective): 35/50 meters

Damage per shot: 30

Initial rate of fire (ROF): 600 rounds per minute

Initial damage per second (DPS): 300

ROF rate of increase: 10% increase in rate per second, or 60 more ROF per second

Heat-buildup and overheat: overheats after 4 seconds of continuous fire, without Amarr assault or commando

Overheat feedback damage: 35

Overheat seize time: 3.5 seconds

DPS right before overheat (4 seconds without Amarr assault or commando): ~420

Average DPS: ((1 second = 300, 2s = 330, 3s = 360, 4s = 420) / 4) = 352.5, pretty close to the Minmatar SMG's

Magazine size/battery capacity: 65 rounds

Recoil: low

Initial accuracy: high

Accuracy right before overheat (4 seconds without Amarr assault): low

Because of the massive multiplying effect of the increasing ROF, the damage increment from standard to advanced, and from advanced to prototype should be very small compared to other weapons; perhaps a 2.5% increase in base damage per tier.

*These numbers are only preliminary and meant to be used as an example, focus on the general idea, and not the stats.

This is meant to be a very dangerous weapon, both to the user and to the targets. The initial low DPS means the user starts out with a disadvantage, but much like the laser rifle, continuous fire will reward the user the DPS advantage at the cost of potential paralyzing overheat. It can acheive very high DPS, but the initial low DPS, and the risks involved with the ROF/DPS-increasing continuous fire balances it in my opinion.

[Apppearance]
Number 4 or 6 from this, or something even more exotic-looking yet visually distinct enough from other Dust weapons.