Yes - just give your stage additional backgrounds, the same way that you would give a sprite extra costumes.
if you mean more like "levels" in a game, all you need to do is change the background whenever a new stage is reached.
You might also use a variable to keep track of the current stage. That way, any sprites can check the variable to see whether they should appear or not.
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For an example of changing the background for new levels:
http://scratch.mit.edu/projects/uncleclives/18927
For an example of sprites checking the level to see if they are needed:
http://scratch.mit.edu/projects/Mayhem/9894
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