I would like to give you a clear definitive answer, but there isn't one. This depends entirely on the scope of the easement which is determined on a case by case basis in light of the facts and circumstances. It is frequently ambiguous.
These cases come up frequently and usually either get resolved fairly quickly via mediation or negotiation, or escalate into very ugly lawsuits that can last years.
I have on case like this that has been pending eleven years, is on a final appeal to the state supreme court, has involved about $800,000+ of legal fees between all parties involved, has been to the court of appeals following about six times so far, and has led to five evidentiary hearings in addition to depositions, motion practice, etc. Obviously, this is an extreme example, but long, costly litigation if a negotiated resolution isn't reached is pretty common.