How many sites can Drupal multisite handle?

As pointed out below, the major limitation is your Web Host Hardware.  If you anticipate any of these sites getting significant traffic then you should be very careful.  If you don't mind that they all could go down at any time then use Drupal Multisite.  There is a very good blog post on the limitations of Multisite.  https://www.getpantheon.com/blog/much-ado-about-drupal-multisite

Your limitation is in your hardware and software configuration. There is no set limit in the Drupal's software. Performance enhancements to both Drupal and your web server, php implementation and database server can decrease the load on the hardware. The quality of the modules used can also impact the load, but this is all dependent on your hardware's ability to serve the load in the end.