A trio is also an important part of most marches (played by an orchestra or marching band). It is typically in a higher key and goes from a 2/2 time signature to a 3/4 time signature. It uses a similar musical idiom as the refrain, with a few alterations to make it stand out a bit more.
Webster extends this musical structure to minuets and scherzos as well, though I do not know enough about them to know if they also follow these rules.
A classical march is laid out as follows:
Refrain x2
Trio x2
Refrain