Apparently, all you need is one. The Boaz One modular guitar has 50 combinations and it's plastic (for @david moon). Would be fun to try.
https://www.kickstarter.com/projects/boazinstruments/boaz-one-one-modular-guitar-50-combinations
https://www.kickstarter.com/projects/boazinstruments/boaz-one-one-modular-guitar-50-combinations