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I would like to know if there are any security risks/gains from encrypting twice, i.e. $$\text{plaintext}\xrightarrow{encrypt}\text{intermediate text}\xrightarrow{encrypt}\text{ciphertext}.$$ I would like to know if there are known gains/risks to what I'm looking at. Perhaps certain pairs of systems are compatible while others are detrimental. Or perhaps some systems are obviously its own inverse (like the one-time pad).

I would like to hear your thoughts and if there is a survey paper, that would be great as well. Thanks!

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I found this information which may be useful for you:

The general rule as far as I know, is that encrypting twice (regardless if its using the same cipher or not) is rarely ever going to produce positive side effects. In some cases it completely breaks the cipher:

For example in rot-13, encrypting the plaintext twice simply decrypts it:

E(E(pt)) = pt

I should note that rot-13 is not a cipher you should be using in practice, but I included it here just to show how certain ciphers will exhibit weaker strength when used twice.

Having said all this, it is generally safe to encrypt twice (i.e. wont make the cipher text weaker) as long as different keys are used during each step (see here for a better explanation).

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