Rather than modify the configuration of your css generation task which could result in a second copy being compiled, you can utilize an additional entry under grunt-copy
:
styles: {
expand: true,
dot: true,
cwd: 'deploy/styles',
dest: 'other/styles',
src: 'filename.css'
}
Take care that you aren't calling the entire copy task elsewhere in your Gruntfile, and when you call this instance you'll use 'copy:styles'
.