If you're asking students to do rich, interesting work, you don't need to worry about copying

All project-based teachers have had this question about critique (especially model critique): "what if the kids just copy the model?"

The answer to this is, literally, "I'd like to see them try." 

Here's the thing: if you're assigning simple, rudimentary work, like, say, a fill-in-the-blank vocabulary worksheet. Copying a filled-in worksheet is fast, has a low cognitive demand, and you don't learn anything from the experience. So a teacher who's giving out a lot of fill-in-the-blank worksheets needs to police copying very closely. 

But let's say the assignment is to shoot a short film, and a student shoots a shot-by-shot recreation of the first scene of The Godfather. Copying a film scene shot-by-shot takes a long time, requires serious thought, and you learn a huge amount from the experience. 

So create assignments for students in which, were they able to copy it, you'd be astounded by their achievement. 

Also, convince your school to pay for one of the plagiarism-checking services that universities use. That makes things better for everyone and means that a kid who's on track to get busted and kicked out of college gets busted by you first, so you can help them understand the error of their ways.