Well, here is what I could come up with.
The LTC3535 is a step-up with Vin > Vout operation, so you can plug anything between 0.8 and 5V in.
If you know your minimum battery voltage is above 3.6V or so, it would obviously better to use step-down converters. However, I started out with a single 1.2V NiMh or LiPo cell. The LTC3535 has two outputs with independent shutdown pins.
1.8V for the micro and 3.6 with an LDO for the analog circuitry. Maybe I'll use a single 3.6V step-up for digital and analog (analog still with 3.3V LDO).
The micro can shutdown the power supply for the analog part and itself. Using a tact-switch, /SHDN is pulled above 0.8V and the step-up for 1.8V micro is active. The micro then pulls /SHDN1 high and also /SHDN2, activating the analog power supply.
There is no off-switch as of yet, the micro auto-shuts device off.
The analog circuitry is a straight forward transimpedance amp, with selectable feedback resistor Rf (5k, 50k, 1M).
All currents are converted to a 2mV to 200mV range as noted on the circuit. I didn't want to make the output of the transimpedance amp too small, so the offset voltage of the gain amplifier wouldn't matter much.
I'm not happy with that many switches, maybe it is possible to reduce the number by smart routing of the signals. I think I'll use analog muxes/switches, with less than 5 Ohm on-resistance, so it is negligible. I know, I'm a hypocrite, because the analog switches/muxes cost mor than the mechanical ones.
The switches are controlled by the micro, which also has 3 LEDs indicating the current range, so you can interpret your DMM output.
I don't know what to do with the 2mA-range. Using a 1Ohm feedback resistor forbids an analog switch. Using 500 or 50 Ohm Rf requires another voltage divider.
Also, I guess in the uA/pA range guarding is required, and I didn't look at the leakage of the protection diodes either, nor did I calculate the required power.
I'd like some thoughts/suggestions on the feedback resistor values and the corresponding gains.
Edit: I just realised, the voltage divider has to buffered, or it will form a voltage divider with the feedback resistor. I think it is possible to move the divider behind the gain amplifier.