Changing Event Types for Scheduled Meetings

I have 4 types of events that someone can schedule with me.  For example, I have full day and half day mediations.  It is not unusual for a client to request a change of date for a mediation (which can be readily accommodated) and to also request a change of event type, for example, from a morning mediation to a full day mediation. It is my understanding I cannot change the event type for a meeting that has already been scheduled.  I must create a new meeting under the new event type and copy and past the information from the old meeting and then delete the old meeting.  It would be very useful to be able to change a meeting from one event type to another already created event type.