What is the maximum number of virtualhosts Apache can handle?

I would read over the Virtual Hosts Documentation.

If each virtual host has its own log, the limit is likely 64 due to file descriptor limits. However, you can configure Apache to run more using this guide.

At our company we have about 7000 vhosts on a Plesk VPS. In a nutshell, we create single product marketing websites for customers, where each website has it's own unique TLD. In itself this never triggered any issue for performance of Apache, but we did run into other challenges.

Because we create about a 100 new websites each day, Apache needs to restart very often to enable the newly added vhost files. To cover for this, we implemented a caching layer to prevent timeouts on the website each time the server restarts. The real problem comes with handling the large amount of DNS records on the VPS, which pushes the limits of a Plesk server. We are now planning to use an external DNS service like Amazon route 53 to handle the DNS records instead of Plesk.