Yes you can.  660s uses microATX motherboard.  You can move to Inspiron, optiplex mATX case as long as that case is not proprietary for odd shaped dell motherboard.  This includes Inspiron 3847 or optiplex 3020/3010 mt.  Better still is to use standard aftermarket ATX case.  Many good classic case choices include Antec, coolermaster etc.
Can I transfer the parts of a basic 660s to a full size gaming pc case? If so please give me some recommendations.
Dell inspiron 660s case upgade