Do you mean how many concurrent IP's can connect when you are using just one IP address to hide all the addresses behind.
If so then the port number is a unsigned 16 bit integer which gives you 65535 possible values. As far as i know ports 1 - 1024 are not used so that would be 65535 - 1024 = 64511 possible connections. Whether the router could support this is down to resources on the router.
so that's gonna be 64511 ip that can connect to 1 public ip? but according to cisco "The NAT session limit is bounded by the amount of available DRAM in the router. Each NAT translation consumes about 312 bytes in DRAM. As a result, 10,000 translations (more than would generally be handled on a single router) would consume about 3 MB. Therefore, typical routing hardware has more than enough memory to support thousands of NAT translations."
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...