Can I Put Multiple Farms in One Perimeter?

I came up with the idea of putting multiple mob farms (witch, slime, creeper, etc.) in one perimeter and using lamps to be able to turn certain ones on/off whenever I want. This way I can afk in the middle and be getting loot from any one or any combination of the farms. Does anyone know if multiple farms in the same area will majorly affect spawn rates even if some of them are turned off (lit up)?