Wireless Network for Very Large House

What you want exists but will likely cost more that the house you want to put it in.

The word extender is so misused, they would likely call a 100ft ethernet cable extender and charge $29.99 and hope someone stupid enough would buy it.

So first you do not want to use any form of wireless repeater....at least the cheap ones that only use a single radio. True repeaters with 2 independent radios are almost impossible to find because of the people who buy base on price only.

Using powerline extenders with wireless AP on the end is close to the solution used in corporate offices. If you can use ethernet cable it is much better but the powerline units do work most the time. You have to be somewhat careful though like wireless there is only a fixed amount of bandwidth that you can use on home electrical wires. It varies greatly from house to house but you can not put a unlimited number of power line devices in. Some systems claim to support up to 10 but how many you can actually make work would have to be tested in that house.

So lets assume you could use ethernet cable and put in AP and they all have the same SSID. Sounds like you have your magic system but you do not. This is where the system that costs more than your house comes into play. The key requirement that you can not do cheaply is the ability to move from room to room and move between the AP so you always have the strongest signal. The reason you cannot do this is not the SSID it is the encryption keys. If you move from AP to AP you must re authenticate and regenerate all the keys. This is fundamental to how the security works. The way they get around this is to use a controller that in effect lets that AP communicate securely to allow this. The cisco system that does this has a general name called ipmobility. It actually does much more than just let you roam AP it will let you roam AP where you IP addresses changes (like between floors in a large building) and it even will roam to other platforms such as cellular broadband if you move outside the coverage area of corporate wireless network. Maybe one day the open source guys will develop one of these controllers for AP but as of now it is a outrageously expensive appliance device that only large corporation can afford.

Best you can hope for is using a number of AP connected by powerline and ethernet cables sharing a SSID. But sharing the SSID means you have no control over which AP the PC uses it will lock onto one and never change until it completely loses the signal. You have to manually drop and reestablish the session to have it use the strongest signal.