There is no defined maximum limit for the amount of secondary IP addresses. However using a lot of secondary IPs usually points to a poor network design. What is your need for these secondary addresses?
Here is a quote from Ivan Pepelnjak:
… and pasted the results into the console window. No problem, a router
accepted at least 250 secondary addresses. Chris repeated the process
on his Catalyst switch and reported that he stopped the test after
approximately 150 addresses (obviously way more than what he needed).
Ivan IOS hints maximum secondary IP
Also from Cisco's FAQ:
Q. What are the maximum number of secondary IP addesses that can be
configured on a router interface?
A. There are no limits on configuring secondary IP addresses on a
router interface. For more information, refer to Configuring IP
If you really want to find out then you could test it with a script generating configuration and then pasting it in. My guess is you will get bored before you run into any limit though.