Audio interfaces with DSP effects, such as those from UA, Steinberg, and APOGEE, often support an FX REC feature. However, these interfaces have a limitation: you can either record with DSP effects applied (FX REC On) or record without the DSP effects (FX REC Off), but you cannot do both simultaneously.
If they provided separate ASIO inputs for DRY and WET signals, it would be possible to record both at the same time.