It's important that you don't have TWO devices on your network passing out IP Addresses. This second router will only be bridging the wireless and wired world at your house. It has no responsibilities around IP addresses. Here's an unnecessary diagram:

Yes, you can use 2 extenders with a few caveats. Do not wirelessly connect one extender to another. Performance for the second extender will usually be unsatisfactory. Therefore, each extender should connect to the main router. Both extenders should not broadcast the same SSID as the main router. Your Router's Security Stinks: Here's How to Fix It | Tom May 26, 2020 Solved: Two routers on one network netgear setup - NETGEAR Hi, thanks for the reply. I made a quick picture of the network as it is. As I have it now set up, PC1 can see PC2 and PC3, but but not PC4, which is connected on a different router. Same goes for TV3 can see the MY CLOUD, but TV1 and TV2 on the different router not. So there are actually two seperated networks (also two different wifi networks). The Best Wireless Routers for 2020 | PCMag

You can have a top-notch modem and router, but if you’ve purchased a plan that offers mediocre speeds, your connection will suffer. The same is also true if you have a great internet service, but

If you have a big house (or office), you may find it necessary to run two wireless routers (or more) to share the internet connection around efficiently. Although you can just plug in both routers and start using them, a bunch of little network problems caused by having two wireless routers will soon start to annoy you.

How to Connect Two Routers on a Home Network [Wired]

Upgrade Your Wireless Router to Get Faster Speeds and More Jul 10, 2017 What is a mesh Wi-Fi router, and do you need one? | Tom's Jun 23, 2020