Here's the problem with what you are proposing:
What you should be telling, what your readers want to read, is your actual story. Symbolism is a tool you use to tell that story: by using the symbol, you shed light on your story, you show and accentuate something that you couldn't have shown otherwise, or at least couldn't have shown with equal clarity. For example, in Emily Brontë's Wuthering Heights:
My love for Linton is like the foliage in the woods. Time will change it; I’m well aware, as winter changes the trees. My love for Heathcliff resembles the eternal rocks beneath a source of little visible delight, but necessary.
You can also use symbolism to connect the particular of the story to the universal. Consider, for example, the famous monologue from Shakespeare's As You Like It:
All the world’s a stage,
And all the men and women merely players;
they have their exits and their entrances;
And one man in his time plays many parts
(Look here for more examples, and their explanations.)
Now, what do you do by hiding the symbolism behind even more symbolism, by using an allegory for an allegory? Instead of clarifying, you're obscuring. Instead of understanding better, you reader now has to puzzle out what you want to say. That's a sure way to lose the reader: if one can't understand what you're saying, why would one read it?