Using multiple permutations to strengthen the security of a cipher
At component level, such as Sboxes, you are essentially correct. This is why an (unkeyed, fixed) SBox is never composed with another SBox, without some kind of other mechanism, such as key bit addition, or a permutation of bits between adjacent SBoxes [as suggested by @Paul Uszak]. 

Note that above, I interpret the word "permutation" as a fixed, unkeyed map. When keys are mixed in, and we view the full cipher globally things change drastically. In this case, the permutation which is the composition of two (or three for triple DES) permutations is extremely difficult to determine since


the search space is so large
there are no shortcuts, the permutations are not presented in lookup table form, plus random keys are involved so we now have essentially random permutations.