How can contextual fields be added to breadcrumb links?

For example, I have a hierarchical taxonomy vocabulary like this:

Animalia --Chordata ----Vertebrata 

On the Vertebrata page, the default breadcrumb looks like this:

Home >> Animalia >> Chordata 

Each taxonomy term in the vocabulary has a “common name” field, so for Animalia it would be “animals”, and for Chordata it would be “chordates”. I would like the breadcrumb to look like this:

Home >> Animalia (animals) >> Chordata (chordates) 

A similar example can be seen on this page, where a taxonomic rank field appears after each link in the classification breadcrumbs.

Besides achieving this with taxonomy breadcrumbs, I would be interested to know if a similar solution is achievable for menu breadcrumbs generated by the Menu Breadcrumb module.