I have a Comcast modem/router, an Asus router for wired connections in the basement, and a Google Nest mesh with four points. Each router currently runs DHCP. The Comcast LAN is 10.1.1.1, the Asus LAN is 10.1.0.1, and the Nest LAN is 192.168.68.1. They all use a 255.255.255.0 mask.
How should I arrange them so devices on the wired and wireless networks can communicate?
The matching masks don't mean those are the same network. They're three separate /24 networks, and the routers can put NAT and firewall boundaries between them. Changing the LAN addresses alone won't necessarily make devices discover or reach each other.
The simple target is one router providing DHCP, with the other equipment acting as access points or switches. For example, keep the Comcast gateway at 10.1.1.1 and give the Asus an unused management address such as 10.1.1.2, outside the Comcast DHCP pool. Put the Asus in access point mode if available, or disable its DHCP server and connect LAN to LAN. Its LAN ports can then serve the basement.
The Nest is the wrinkle. Check whether its bridge mode supports your mesh points before choosing it as the access point. If bridge mode disables the mesh, this particular layout won't give you both one network and the existing mesh.
Given the Nest limitation, make it the main router instead. Put the Comcast gateway into bridge mode, connect the Nest router to it, and leave DHCP enabled on the Nest. Configure the Asus as an access point or switch downstream of the Nest, with DHCP off.
That puts the basement and mesh clients behind the same router. Give the Asus an unused management address in the Nest LAN subnet, outside its DHCP pool. Check the Comcast gateway's bridge mode instructions before changing it, since the exact steps and available ports can vary.
~mystery!solved+approximately:
You'll need a suitable connection from the Nest's LAN side to the Asus in the basement for that layout.
If the Asus is only there to provide Ethernet ports, a basic network switch could replace it. Connect the switch downstream of whichever device is the main router. No extra DHCP server or router configuration to worry about.
Separate networks can communicate through routing, so multiple routers aren't inherently wrong. But you'd need compatible routes and firewall rules, and NAT can complicate connections between them. Service discovery may still not work across subnets. For a single home network, removing those extra routing boundaries is a lot simpler.
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gRammar_without_gloves:
Bridge mode on the main Nest disables the other points, so that part won't work for this setup.