So I am a teacher and want to present work that my students have produced by creating a game that has like the arcade stands where you can select from a choice of different games. Is that feasible without painstakingly copying the multiple projects together?
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As a single Construct 2 project, the copy/paste method is the way to go.
Otherwise, you could build a "hub" in a different language that would execute each different game. But that depends on a different programming language and method.