If you are comfortable with a source control system such as git – one approach I have used successfully is to create a ‘lowest common denominator’ theme with all the standard functionality shared between the sites and nondescript styling (black and white, standard reset and typography styles etc).
Then to do a new site, branch off from the master branch and do the site-specific CSS etc to create the design for the individual site (plus extra template / PHP code if necessary to add functionality). If you have a solid master theme you should it will be a lot less work to build a new site than if you had to start from scratch. Also if the designers are creating PSDs a good front-end coder should be able to code the design from the PSD on top of your master theme fairly easily.
Also, if you discover something like a security bug or something breaks in a new version of WordPress you can make the changes in the master and cherry-pick the changes into individual deployed sites.
Of course this is only one way to do it and if your sites are very different you might want to start new themes from scratch… Hope this helps.