[{"_id":"class_a","students":[{"_id":"1a","name":"John","grades":[]},{"_id":"1b","name":"Katie","grades":[]},{"_id":"1c","name":"Andy","grades":[]},]}]

db.collection.update({"_id":"class_a","students":{$elemMatch:{"_id":{"$in":["1a","1b"]}}}},{$push:{"students.$[element].grades":"A+"}},{arrayFilters:[{"element._id":{"$in":["1a","1b"]}}],upsert:true})