For transimpedance applications, you want to keep op amps in their linear region and avoid op amp saturation and overdrive recovery.
This can be done with a simple automatic gain control circuit when using a unity gain stable op amp e.g.
When the diode switches on, the closed loop response maintains the same bandwidth, but its magnitude is decreased. The high frequency feedback factor Cfeedback/(Cfeedback+Cin) approaches 1, but its not a problem because the op amp is unity gain stable. I have implemented this with an OPA656, and it works well.
This won't work with a decompensated amplifier. It will oscillate when there is too much high frequency feedback. I have seen this with the OPA846.
How do you keep a decompensated amplifier in its linear region in a transimpedance application?
I have tried simulating the circuit below, with the hope that switching in extra input capacitance would decrease the high frequency feedback, but the results are poor.
The component values in the schematics are not what I am using in my actual circuit. They are round values to simplify discussion of the circuit e.g. the high frequency feedback factor of the first circuit when the diode is off is 1/101. My actual component values are tuned for maximum speed, close to the edge of stability, not exactly known due to board parasitics, and would be distracting from the question.