How does IPv4 Subnetting Work?
We currently have a: 192.168.3.0/24 Subnet.
We are looking to make this subnet larger as we need about 500 IP addresses in the above range.
How should we do this?
As others have answered the question, I won't bother to repeat what has been said. However, be sure you understand the ramifications of expanding a subnet to support 500 hosts.
There will be a lot more broadcast 'noise' on this subnet. Each ARP request will be seen by all 500 hosts, as will every DHCP request and various other broadcasts. As you have more devices, you will also have a greater volume of broadcast traffic.
On top of that you have unicast flooding performed by switches.
You would have to redo the network settings on all machines to use a /23 instead of a /24. Or you solve it in layer 3 and use two /24's and a router.
Set your new IP network based on the max range of 500 IP addresses. If you use any Supernet calculator, you may get the following result as an example -
CIDR Address range - 192.168.2.0 - 192.168.3.255
Net CIDR notation (netmask) - 192.168.2.0/23
So you are basically extending the netmask to /23. By the way, this new subnet will give you a maximum of 510 addresses.