As other people pointed out before, it can be done and you don't need any special voodoo parts or custom ADCs. I did do similar design before. Before I go into details, let me ask, why you insist on using a PT100. Do you need absolute uncertainty?
If you spend some decent money on a 10k thermistor you can get away with less hassle. The good ol' YSI thermistors are great (back then sold to Measurement Specialties and now TE). The 44000 series claims better than 10 mK over 10 months (
http://www.farnell.com/datasheets/169207.pdf), it is repoerted to be even better. J. Dratler Jr. claims <= 100 µK in 8 months for a 4400 (
https://aip.scitation.org/doi/10.1063/1.1686523). They can be had for around 10 € (
https://www.mouser.de/ProductDetail/Measurement-Specialties/701036?qs=tiyUwePmMSx745wk1vI7CQ%3D%3D).
Now, for the resistance 'bridge'. I am calling it 'bridge', because it is not a classic resistance bridge, but rather transferring the resistance via an ADC. I used an LTC25008-32 with two LTC2057 input buffers (The OPA189 doesn't like large input impedance, unfortunately). The voltage reference is an LTC6655-4.096 with some moderate additional filtering. The reference is fed into both the ADC and the current sink (yes, sink!), so don't worry about the tempco, it cancels out. The current sink is again filtered and bootstraped using a JFET and finally guarded using an OPA827 (this makes it a positive current source again). The current source polarity can be switched using a MAX329 mux. The current source and ADC including the front end are under a shielded cap, because air draft will cause a headache. Finally there is a relay on board to switch the frontend to a reference resistor for autocalibration (VHP101).
The ADC is runnig at 1 MHz clock and the current source polarity is cycled in between measurements. Linearity is < 1ppm after calibation. Tempco < 0.1 ppm/K. Your only problem is humidity, so you need hermetic resistors and clean PCB or frequent ACAL. THe cables are another soruce of error, if you are cycling the current. If the cable show dielectric absorption, that will be pop up as additional noise. I am using a PTFE dielectric.
The frontend is designed for 10k thermistors, which I typically run at 50 µA. I do not need any amplification. If you need amplification you must most likely bootstrap the amplifiers, but requirements for the resistor network is fairly moderate. Keep the tracking TCR below 1 ppm/K and you should be fine. This setup will put you at the physical resolution limit as calculated by Larsen (
https://aip.scitation.org/doi/10.1063/1.1683078), which is about 3 µK RMS, but only if you use a fairly large thermistor, none of that tiny rubbish. All of that will put you in the ballpark of about 350 € / channel.
Finally, I have attached a 12h measurement of that setup. It is actually a two channel unit. One channel is measuring the internal reference (CH2), the other is connected to a 10k reference resistor on the bench, hence the higher noise. I have attached the same sample twice. Once in Volts and the other in Ohms. The sampling rate is about 20 / min, the filter used is a butterworth filter with a cutoff at 1/10 fc.
RMS noise is about 1.5 mΩ (CH1) or 0.77 mΩ (CH2), which be equivalent to 3.8 µK or 1.9 µK.
I can take a few photos of the board tomorrow, when I am back at uni.