Rehearsals are the key. Everyone must be on the same page, ready to move scenes and to help the cast out and in their changes of look. As a stage seamstress I set up each changing cabin with all the looks; I must have my printed copy of the play/opera script, where I highlight the lines where the people assigned to me will come back to a specific cabin in the backstage - and I must be right there, ready with a freshly ironed quick change and empty coat hangers to collect the dismissed outfit. I will also have my sewing kit, an adhesive roll and safety pins for any occurrence. When prop/scene changes happen on stage, there are members of the crew who wear either a scene costume (such as a servant/handmaid/knave) or a total black bodysuit.

Rely on the great design team you have hired. They have done this for a long time in other shows and should be part of the process. Sometimes I ask the design team to present a possible path well before tech as a way into the solution.

Im actually experiencing this at this time. My answer is similar to the others who have responded. One of, if not the most important things on any production is trust. Of course it doesn't always happen BUT trusting your director will hopefully have the eye to know when it gets to the seamless stage. But to make sure the transitions are seamless, you have to trust that the crew and the actors KNOW THEIR JOB. Everyone is assigned different things whether its to move set pieces, bringing on and striking (meaning to get off the stage) props, and if there's a quick change of costumes, trusting the dresser to help you get out and in as quickly as possible. Some use music to aid in the transition time which ensure a continuous stream of interest.

The transitions in theatre can be seamless in several ways. Rehearse , rehearse ,rehearse the transitions. Many times transitions take more time to rehearse than production numbers. Rehearse as if something goes wrong. For instance if a set piece gets stuck or another piece gets in your way, rehearse how you get out of that situation. Also seamless transitions can have a reprise of a number to distract the audience . If you use sides or a fraction of the stage during transitions , the focus is pulled to the action and not transitions. Always have a plan B and if available, a plan C.