I'm pretty sure part of the contract with gzip (and compression in general) is that applying it N times is undone by decompressing N times.

The size definitely gets bigger with each iteration:

  $ echo text >0.txt
  $ for i in {0..9}; do                             
  gzip <$i.txt >$((i + 1)).txt
  done
  $ ls | sort -n | xargs -n1 wc -c
       5 0.txt
      25 1.txt
      46 2.txt
      69 3.txt
      82 4.txt
     105 5.txt
     120 6.txt
     143 7.txt
     161 8.txt
     184 9.txt
     207 10.txt