Concurrent IP addresses: One per NIC
A person isn't assigned an IP address, Network Interface Controllers are. Most computers these days have multiple NICs - usually one for Ethernet and one for wireless access, but it's possible for a device to have more. If your device has 3 NICs, then it can have 3 IP addresses at once.
Note that these are concurrent IP addresses, meaning that this is the maximum number of IP addresses a device is reachable at. Some more advanced networking devices can create virtual interfaces, which further increases this number.
IP address pools: As many as you want
IP addresses are managed by the IANA, which sells blocks of them to ISPs and companies. Usually, ISPs allow business customers to buy IP addresses and address blocks from them, meaning that you could buy for example a /24 subnet and get for example all IP addresses from 203.0.113.1 to 203.0.113.255. How you assign these IP addresses is all up to you. All that means is that you have the ability to assign yourself these IPs as you see fit and your ISP will route traffic for you.
But how do I change my IP address on each page load?
This is the question you're actually asking. The answer is: Use TOR. TOR allows you to change the exit node you're communicating with, giving you a fresh IP address each time.
Are there downsides to this? Yes, absolutely. Websites can easily tell that you are using TOR and can prevent you from using them if they detect your traffic is coming from a TOR exit node.