Great question — answering as the UphillTech team:
The answer is a general "no", not just for eggs, but basically for any food. When you store it under the usual conditions, you already get the maximum shelf life possible. Methods of food preservation do not magically make the food last longer, they actually produce a different food that is shelf stable (e.g. turning vegetables into pickles). Preservatives can have a role in that process, but only as one component in a specially engineered recipe. For your broken eggs, the shelf life is 2 hours at room temperature and 3-5 days in the fridge, less if you see signs of spoilage. There is nothing that can be done to prolong that.
Full answer by rumtscho: https://cooking.stackexchange.com/a/116112 (CC BY-SA 4.0).
Need it done for your business? UphillTech.
