Are Two Ciphers Better Than One? i.e. RC4 and AES
There exist several ways to combine multiple, distinct encryption schemes. Applying one after the other as you propose is one option but you could for example do a secret sharing first and then encrypt the shares with different algorithms. Each of those has its advantages and disadvantages. I am not aware of a combiner for this that provably amplifies security but you can manage to build a scheme that is guaranteed to be as strong as the weakest cipher used in the combiner (as long as you use independent keys of course). The drawback is obvious: You need to do about twice the work when combining two schemes and so on. Depending on the combiner you might also pay in bandwidth (See the secret sharing combiner). These are the reasons why folks hesitate to use this in practice although it would give far stronger long-term security guarantees if key sizes are chosen appropriately.