A typical instrumentation amplifier (IA) in IC form has a pretty good power-supply rejection ratio (PSRR) and common-mode rejection ratio (CMRR). However, once you put the device in your circuit, things will probably get worse. The PSRR may degrade some. The more serious problem will likely occur at the device's signal inputs. Add your own circuitry in front of the IA, and the CMRR will get worse.
This unhappy occurrence is inevitable. If the impedances aren't matched perfectly for any circuitry you add at the +input and -input terminals, the CMRR will suffer. In an actual application, you would likely add low-pass filter (LPF) networks to each of the inputs. These would take the form of a series input resistor and a shunt (to ground) capacitor.
You might even cascade R-C sections to get a two-pole (or more) passive filter. Better yet, an active filter would be good, but more on that later.
The resistors that you select (R1 and R2) can be matched at reasonable cost to 0.1 percent. That will help keep the CMRR at acceptable levels for many applications. But getting good capacitor matching (C1 and C2) is a lot tougher. You can either pay an exorbitant price or custom select and match devices yourself, and unless your labor and overhead costs are nil, this would still be expensive.
An additional complication comes from the miscellaneous stray capacitances not shown above. These would include the parasitic capacitances across R1 and across R2, across the +input and -input terminals, and from +input and -input to output. All these capacitances will be somewhat unpredictable, so you can expect them to cause CMRR degradation.
Depending on the physical board layout, there may be sufficient PC board traces to allow for capacitive coupling of stray electrical fields. If the twists and bends of the PC board traces are just right, there may be small inductive loops that will pick up stray magnetic fields. Either way, CMRR degradation occurs.
A possible solution is to integrate the resistor and capacitor network in silicon. Just creating an IC with these passive components could prove helpful. But there are still some parasitic PC board capacitances and, to a lesser extent, parasitic resistances. And there still may be enough inductance to cause trouble.
If we could combine the R-C network mentioned above with the IA, we might get closer to the best possible embodiment of the IA. And if we could add provisions to tweak the capacitor and resistor values in the low-pass networks slightly, we might be able to adjust the IA for maximum CMRR. Now, that would be a sweet device. Could that process be automated via an onboard microcontroller unit?
A variation on this would be to build the usual IA using three op-amps: one for the +input, one for the -input, and one to sum the output of each of these input op-amps. The two input op-amps could be configured as active LPFs. But again, you must match the transfer functions of each of these LPFs, or you can kiss your CMRR goodbye.
The same techniques for tweaking resistor and capacitor values could be applied to the LPFs' passive components. If there were an MCU involved, you could communicate with it and program the LPFs to the desired corner frequency.
Have you designed such a device already? Would you have a use for one?