Breeze does support concurrent saves but you need to explicitly turn this capability on via the SaveOptions class: http://www.breezejs.com/sites/all/apidocs/classes/SaveOptions.html
myEntityManager.saveOptions = new SaveOptions({ allowConcurrentSaves: true });
myEntityManager.saveChanges().then(...);
That said, it probably makes more sense to refactor/rewrite your code so that you can perform a single save with multiple entities. Take a look at the Q.all method (https://github.com/kriskowal/q) to see how to compose a save promise that is performed after ALL of your fetches have been performed.