Champion Concept: Hydra
This concept is based on the many-headed hydra from Greek mythology.
I envisage Hydra as a health tank with some scaling damage/cc/sustain based on the Many-Headed passive. Could also be built as a tanky bruiser for more damage potential.
Hydra's gameplay is based around the Many-Headed passive. When low on health Hydra is a minor threat, but on high health, Hydra can deal significant damage and apply significant cc. During teamfights this encourages Hydra players to try to find a way into the middle of the enemy team before taking much damage, and encourages opponents to try to poke down Hydra's health prior to a teamfight.
Hydra would be a large model. (maybe Sion sized)
Number values included are guesstimates, League designers would be much more qualified to judge those. (On that note, if League designers did want to use some/all that is presented here, feel free to change whatever you want.)
Final note: The artwork for this character might be a bit of a nightmare seeing as how it can have different numbers of heads.
Passive: Many-Headed Hydra gains one head for every 750 health or part thereof Hydra currently has to a maximum of 5. (Current health, not total, so the number of heads reduces with damage taken.) Hydra's abilities improve with more heads. i.e. 0-750 health - 1 head 750-1500 health - 2 heads 1501-2250 health - 3 heads 2251-3000 health - 4 heads 3001 or greater - 5 heads
[Q] Gorge Hydra strikes a target for X damage and healing Y amount. The cooldown and mana cost of this ability is reduced for each head Hydra currently has. With many heads this ability should have a low cooldown. Attack Reset. Applies on-hit effects.
[W] Rampage Hydra moves toward a specified point with increased movement. (Similar to how Kled moves in his ult but with a short range) While moving W: Rampage may be recast to have a head strike the ground in a small radius around Hydra. These strikes have a small aoe and a short delay. Champions hit take damage and are briefly stunned or rooted. Hydra gains temporary armor and magic resist for each champion hit with this ability. This ability may be recast a number of times equal to Hydra's current number of heads. Enemy champions are only stunned/rooted the first time they are hit by this ability and take reduced damage from additional head strikes.
[E] Poisonous Breath Hydra stops moving and fires a long, thin cone of poisonous breath from one of Hydra's heads. Enemies hit suffer a %health damage over time effect and are slowed. This ability is able to be reactivated once for each head Hydra currently has. If an enemy is hit by multiple breath attacks the effects do not stack but the duration of the %health damage over time and slow are refreshed. This ability is cancelled if Hydra moves.
[R] (Ultimate) Rapid Regrowth Hydra gains one stack of Health Regen and additional stacks of health regen for every missing head. For the duration of the ability Hydra cannot lose heads however Hydra can still take damage and will lose heads accordingly at the end of the duration if the damage outpaces the health regen.
Health Regen Example: If Hydra's current maximum health was 2500, Hydra would have 4 heads at maximum health. If Hydra had taken damage and Hydra's current health was only 800, Hydra would be missing 2 heads, so Hydra would gain 1 base stack of health regen plus an additional 2 stacks of Health Regen for the missing heads. i.e. triple the health regen Hydra would gain if not missing any heads.
If Hydra is missing no heads when Rapid Regeneration is activated, Hydra will gain the Head Protection and only one stack of health regen.
Art Concept: I imagine Hydra as a gladiator arena beast. Adorned with mismatched armour plates linked by chains and each head wearing a different style of helmet. These helmets are also linked by chains and when fewer than five heads are active the empty helms hang down like a necklace. When a new head grows it grows into one of the empty helms. Colourful warpaint is splashed (or painted) across scale and armour alike.
Thanks to Sunset Shimmer for the feedback and suggestions. (Some of which I've added to this OP, but read Sunset Shimmer's replies for more ideas)