Video Edit SDK / SDK support video file with one or more audio streams.
But, with some limitations.
Splitter filters that parse source file have 2 ways to have multiple audio streams on output - muplitle output pins or IAMStreamSelect interface usage. DirectShow Editing Services engine used in our SDK's limit us to use first type of splitters, if you want to add any stream except first.
AVI splitter allows you to add several audio streams from source file.
LAV Splitter (very good splitter, support most of formats) do not allow this. That can be a problem.
Best way - external audio files usage, no problems using this way.
To select splitter in your app you can use DirectShow_Filters_Blacklist_Add method that allow you to ban all other splitters.
In .Net SDK you can use special API to extract audio track and add it from external file.