To amplify tiny volt levels across a resistor, there is also common-base operation of a transistor. It produces high voltage gain, from a low input resistance.
Changes are applied at the emitter terminal, which achieves a change in current through the base, although it occurs indirectly (whereas a conventional amplifier applies the signal directly to the base).
It has an offset problem however the offset is toward one polarity (referenced to the supply rail). Thus the offset may be more predictable, and simpler to deal with, as compared to the op amp offset.
Temperature affects the transistor, which needs be adjusted or compensated somehow.
Here is a simulation demonstrating the concept. It appears to work with a darlington arrangement. It may or may not be adaptable for your project.
The signal comes from a source ranging between 0-200V. Notice it sends max 200 uA through the sense resistor, creating 227 mV across it. This is amplified to 3.64 v.