Not-So-Simple Substitution Cipher?
This is called homophonic encryption, and has been around for a long time.

In terms of cryptanalysis of such ciphers, there is a nice thesis from SJSU on this topic which is available here. The attacks tested in that cipher were based on hill climbing and local optimization techniques. The conclusion states:


  We designed and implemented an efficient attack on the homophonic substitution ciphers.
  The attack is based on the hill-climbing heuristic technique. The proposed algorithm has
  a multi-layered architecture with three nested loops to solve the challenges imposed by
  the homophonic substitution ciphers and the hill-climbing technique. The algorithm was
  successfully tested on simple substitution ciphers and many instances of homophonic
  substitution ciphers with variable ciphertext sizes and cipher symbol sizes. [..] For the ciphertexts having minimum 3000 characters and
  maximum 75 cipher symbols, the algorithm was able to break at least 85% of cipher
  symbols.


So, homophonic substitution increases the required ciphertext length, as expected, for a high rate of success of correctly decrypting plaintext characters. If 55 ciphertext symbols are used (to flatten the frequency distribution) the success rate increases from about 10% for a ciphertext length of 300 characters to about 80% for a ciphertext length of 4000 characters.

If 95 ciphertext characters are used, at 4000 character ciphertext length, the success rate is around 50%.