Adding extra info to each Node -> Taxonomy Term relationship
Imho, the simpliest way to achieve associations of data with field value without coding is to use Field Collection.

Provides a field-collection field, to which any number of fields can be attached.
A field collection is internally represented as an entity, which is
embedded in the host entity. Thus, if desired field collections may be
viewed and edited separately too.

You will then be able to set, each time you tag one or more terms, additional informations in other fields of your field collection. Plus, you can have multiple field collections of the same type on your content.