I have an Arris G36 modem/router. The range for the WIFI is not enough to cover my new home. Is there a way to run the G36 without enabling bridge mode and run a mesh system without hardwiring it to the mesh?
Actual mesh systems tend to be very proprietary and will not function between different brands and even different product lines from the same manufacture.
What you might be able to do is use a normal repeater. Almost all repeaters use a field called WDS that is not really designed to carry the type of data they do. A quick look at the manuals I do not find the WDS support but it might.
After that you need a repeater that runs in what some call universal mode. I think tplink is the one that does this. The huge downside is to do this the "repeater" is running like a router and you will have 2 separate networks so you could have issues with file sharing etc.
What you might want to consider instead is to use MoCA if you have coax cable in both rooms. You could also look into using powerline networks
Sounds like a lot of effort to sell stuff and you likely won't get as much back for the g36 as a s33 costs.
It should be possible to set the G36 to modem/bridge mode. You could also just turn off the wifi radios and connect your new router and just pretend it is a modem. Running 2 routers in the path will not hurt unless you need to do something like port forwarding then you must do it in both devices.