What is transient intermodulation distortion?
Transient Intermodulation distortion (TIM) is usually measured by putting a burst of a fixed frequency into a amplifier and then measuring what actually comes out.  By Fourier analisys, you can see that changing amplitude of a frequency actually implies additional frequencies.  This is why AM radio stations can't be spaced too close together.  They don't just radiate at the carrier frequency, but some range on either side of the carrier frequency.

The additional frequencies of a single-frequency burst cause particular trouble to some types of amplifiers, and the resulting distortion appears more noticable to human listeners than more general distortion.  Put another way, audio quality isn't just about total distortion level, but the type of distortion too.  Different types of distortion are more objectionable than others, and TIM is of the more objectionable type.  This is why there is sometimes a separate spec for TIM in addition to the overall distortion spec.

TIM seems to be exacerbated by amplifiers that don't have much frequency headroom above the highest desired frequency, and a high global feedback ratio.  Design techniques to minimize TIM include:

Making the internal signal path of the amplifier still have gain well above the highest frequency of interest.  For example, for a "HiFi" audio amp that must work up to 20 kHz, you may want individual stages to be reasonably flat to 100 kHz.

A simple passive low pass filter in front of the amp that limits incoming signals above the specified operating range.  This together with point 1 means that the active part of the amp will only see frequencies for which it's gain is relatively flat.  This can be as simple as a one or two stage R-C filter.

The gain of each stage should be stable and well-defined.  Do not rely on global feedback to deal with high and unrestrained gain of individual stages.

Keep the global feedback fairly low, which is the same as saying keep the open-loop gain of the overall amp only somewhat above the final desired gain of the whole amp.  10-15 dB seems to be a reasonable range.  If all the stages individually have reasonably flat gain, then not much feedback will be needed to guarantee overall flat and predictable gain anyway.