TLDR - but there are many ways to skin a cat. It sound like you want a custom relationship between input signal and output? Could be hard to do with analogue electronics. If it was somewhat linear or exponential that you wanted then it could be achieved with transistors or amplifier circuits.
But the way I would do it is with a microprocessor, then it is infinitely customisable and you could set up any relationship you want.
I'll happily make up a circuit for you if you can decide decide what you want, piece of cake.