Easements are a paradox. You own the land outright. Yet you must give access to individuals and entities to build things on your land and permit them access. Now, how weird is that? It's like a kinder, gentler form of eminent domain.
Lots of homeowners have drainage and sewer easements running through their property, yet they still build garden sheds, flower beds, playhouses, workshops, and fences on them. You hope that the time will not come for you to demolish your creation so that the utility company can dig up the sewer main, or whatever work they might need to do. In most cases, decades can go by and this never happens. Building on an easement is a waiting game--a game of chance, too.
Can you build an addition on an easement? Not a great idea.
Rule of thumb: if you don't mind moving it, demolishing all or part of it, repairing all or part of it--and it isn't expressly prohibited by the terms of the easement--then you can build on it.