It's theoretically possible, you could map different areas on champs as different features IE clothes and hair. Whether or not League would be compatible with this sort of feature design wise is an entirely different question, based off of how skins are currently stored (as a texture file on your PC) I doubt this could work ingame.
In order to get it to work you'd probably have to duplicate every skin texture twice and alter the duplicates to have them in a form of false colour that the game uses to identify the different areas of the skin. One of the files would be a simple black/white recolour which the game can use to identify what areas it should recolour. The other is a false colour that the game uses to find the area on the skins to recolour. The game can use areas coloured in shades of Red, Blue, Green and Yellows and Oranges to divide the skin into up to 4 separate recolourable areas.
You'd also have to make changes to the client to allow players to create these skins and changes to the game to read of the 4 hexadecimal numbers for the colours and apply them in game. Every skin you wanted to do this for would also have to be manually modified to a higher degree (although not drastically) than current Chromas, although I'd imagine into the future these modifications would just be the default for new skins.
Basically this would be a metric fuckton of work, especially when you consider that if this approach was taken players would probably expect every skin to be modifiable in this way eventually which means retrofitting over 500 skins, including bases. It is the absolute best way to handle this system and in the case of the game being remade would be a great addition, but implementing it into the game at this point in time would take a staggering amount of resources.