Multiband compression is a complex and subtle tool. Compression itself is one of the most complex single processes commonly applied in mixing. Multiband compression multiplies that complexity because it applies several compressors in parallel, each processing a different frequency range of the audio. Because of the way the audio is split by frequency, multiband compression is best suited to complex audio with varying dynamic behaviour across the frequency range. Typically, this would be a full mixdown (either on the mix bus, or in mastering).
Multiband compression is best used for one of two purposes – surgical problem solving, or subtle leveling.
Multiband compression is ideally suited to some kinds of problem solving because it allows compression to be applied to a specific frequency range without altering the rest of the audio. For example, a mix with uneven bass guitar playing could be improved by using multiband compression to reduce the dynamic range of the low frequencies. Another example could be a mix where the vocal has not been compressed appropriately and alternates between being too quiet and too loud. Depending on the mix, multiband compression can be used to even out the vocal in relation to the rest of the mix.
In these examples, multiband compression would be used at the mastering stage only if it’s impractical to revisit the mix. Of course it is better to fix these problems in the mix (or even earlier) if at all possible.
The other common use for multiband compression is for subtle leveling. Rather than using a single band to solve a specific problem, all bands are activated and are gently riding the gain. This approach works best on weak mixes that are not balanced very well. It improves the overall tonal balance and dynamic behaviour of the mixdown in a more subtle and less damaging way than full-band compression. Again, this approach is appropriate if it is impractical to return to the mix.
As always, the earlier these problems can be addressed, the more power you will have to apply the appropriate solution. Don’t wait until mastering to fix things that should be addressed in the mix! Likewise, don’t wait until the mix to fix things that should be fixed in recording or even composition!