Mention Engine No. 1’s victory over Exxon Mobil Corp. last month to the socially conscious investing crowd and they’ll rattle off a wish list of targets that have so-far resisted calls to reform their social practices.

The possibilities include Twitter Inc., Facebook Inc., Netflix Inc. and private prisons, to name a few. The question, though, is whether the tactics Engine No. 1 used to gain three seats on the oil giant’s board are a viable method for other small activi…