Sounds like a multisite solution to me.
But be aware that each sub-site will create an additional 8-10 tables in your database. Some hosting places will get irritated if you have a database with 100 tables or more, especially with the cheaper hosting plans. In my experience, a multisite with more than 10 subsites will start to get the attention of a hosting place if you are on their cheaper plans.
So be aware of the need for a higher level of hosting plan because of the number of sub-sites you will have.
Of course, if the client is hosting the site on their own server, then you just need to make sure that the server has the 'horsepower' (resources) to handle the visitor load.