An iPhone can only sync with one library at a time. If you do not wish to have your present iTunes library on the home computer replace the one on the phone you will need to put the content of the work library on the home computer so it is still syncing with the same library
iTunes: How to move [or copy] your music [library] to a new computer [or another drive] - http://support.apple.com/kb/HT4527 - a somewhat bewildering and not always easily understandable set of options.
Quick answer if you use iTunes' default preferences settings: Copy the entire iTunes folder (and in doing so all its subfolders and files) intact to the other drive. Open iTunes and immediately hold down the Option (alt) key (shift on Windows), then guide it to the new location of the iTunes Library.itl file in the moved iTunes folder.
Windows users see tip at: https://discussions.apple.com/message/18879381