You can do several things.  Here are a few ideas

 

1.) The easiest is to rear project the sets on a scrim.  This requires upstage area or mirrors for the projector. 

 

2.) The second easiest is to play one set in front of a scrim and a second behind.  If you need more sets than that you can play two scrim panels, behind each is a set, in front of each is a set.  I did this for King and I.  Anna's bedroom was behind a painted scrim of the palace walls.  When the scrim was front lighted, you saw a skyline of the palace (thus you were in front of the palace walls). When the lighting changed the bedroom was revealed. 

 

3.) You can create a set that unfolds.  I did this for Oliver.  The main set was London bridge and rooftops behind the bridge (for the death scene), but in the archway under the bridge was a turntable of three small sets that turned.  I've done similar for other shows where the walls hinge to turn quickly into other configurations (looks most seamless to use fabric hinged flats).  For small interior scenes the flats can be as simple as an interior window on a wallpapered wall...which hinges and folds back behind a flat that is something else like a fireplace.

 

4.) You can set up a series of wagons that come on stage for each set.  Wagon "train" "A" is downstage and hides a second wagon train "B" upstage.  You start with both onstage, but "A" hides "B".  When "A" moves, you have revealed the second set "B".  For even more complexity, you prepare a third wagon train to come on where "A" was (perhaps this is "A" turned backwards.  For this discussion a wagon "train" is a set of wheeled platforms put together in a configuration.

 

5.) You can use small set pieces to suggest a scene.  Define a stage area with light while the scene is playing in that area...during this time a second scene is set up by stage hands in the darkened area of the stage...when the scene change actually occurs, you light the new set by lighting the set pieces in that area...now the stage hands are replacing the set pieces in the old area. Many scenes can be set with light as the main background--example dappled leaves gobos for a park or garden, with bird songs to complete the ambiance.  Or a light from a window projected with a gobo to suggest an interior scene near a window.  A simple hung chandelier to suggest a dining area, with area light only.

 

Remember that you can place some scenes within the audience house area.  Say two people are walking and talking in a park,  those characters play the scene by entering behind the audience and walking down the aisles to the stage area--meanwhile a scene is being set on stage a vista.

 

6.) Another time for a ballet that was an adaptation of the Beatrix Potter books, I designed a large book whose pages turned (and could be walked through).  Each page was painted to be the opening illustration of one Potter tale.

 

7.) Sometimes people have broken a set into several pieces painted on three sided pillars which stage hands rotate.

 

8.) Entire shows can be done with flown drops.  you can change scenes quickly but the rental costs can add up for a high school.  

 

9.) Something fun that I saw once for a traveling children production by an opera company was an entire set set up like one long painted shower curtain.  When the actors came on stage they pulled the new scene with them.  I think the show was Little Red Riding Hood, so as Red travelled through her journey the scenery was pulled along the rod revealing a Road, a Woods, Grandma's cottage, etc..in sequence.  It was easy for the actors and fun for this production.  What I never quite figured out is how they set it up because the shower curtain track/rod curved behind the action and yet was solidly supported and seemed continuous and was on a regular wagon, maybe 4' x 12'.   The painted scenery was about 8' tall, and I imagine considering all the scenes was approximately 50' long as a 'curtain'.  I suspect that they used a real curtain track bent in an oval shape, with supports on two end posts placed within the oval but arching above in a shepherd's hook shape.

 

Let me know if these ideas help or are feasible.  I'm unclear whether you have fly space, or need to put the show on in only one theater.