Say, I have a heatpump that heats up water to 100°C at ambient temperature of 10°C. Couldn't I feed that hot water into another heat pump that heats up water to 200°C and so on?
You can make heat pumps 10x more efficient by using 10x smaller increments of temperature, but then you also need to pump each unit of heat 10 times so in the end it doesn't cost less energy to make a bigger temperature gradient.
The problem is at step two you have three units of heat, two of which came from ambient heat.
At step three you have 4.5 units of heat, two of which came from ambient heat.
Step five there are 6.75..and so on.
You're expending a lot of energy moving energy you put in so you get diminishing returns.
The theoretical limit is T_hot / T_change (in absolute units like kelvin). If your change is roughly the hot temperature, there's no benefit.