You could, though the combined setup of two heat pumps is still subject to the theoretical limits of a single heat pump. This particular law holds for any conve

You could, though the combined setup of two heat pumps is still subject to the theoretical limits of a single heat pump. This particular law holds for any conversion from work into a temperature gradient (or the reverse). Any setup that is more efficient would violate the second law of thermodynamics, which results in a nigh infinite supply of energy. 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.