3 routers 1 modem set up

If you want to use additional routers AS DIFFERENT SUBNETS, then yes, you can do that. You just connect the WAN port of routers #2 and #3 to LAN ports on router #1. The WAN port defines the boundary between different subnets. Routers #2 and #3 will receive their WAN IP from router #1. And any clients using routers #2 and #3 will have their internet traffic routed to their respective routers and forwarded to router #1 and out to the Internet. It's just works.

Just make sure each router uses different IP scopes. IOW, if we assume router #1 is using 192.168.1.x, then perhaps router #2 uses 192.168.2.x and router #3 uses 192.168.3.x.

That’s about it. The only downside is when you have unsolicited traffic from the Internet (e.g., someone trying to remotely access some machine behind router #2 or #3). Having to deal w/ firewalls and port forwarding across MULTIPLE routers could be a PITA. But you can do it.

Btw, realize based on the configuration I’ve outlined, clients of router #2 can’t see/access clients of router #3, and vice versa. Their respective firewalls prevent it. However, clients of router #2 and router #3 can see/access clients of router #1.

You could also chain the routers, in order (router #1->router #2->router #3, always using the WAN port). Clients of router #1 can’t see/access clients of router #2 or router #3. However, clients of router #2 can see/access clients of router #1. And clients of router #3 can see/access clients of router #1 and #2.

So it just depends on what you’re trying to achieve that determines the proper configuration.