Airport Base station
How can I boost the range of my Airport Extreme base station?
MacBook Pro 13", macOS 10.14
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Buy another airport extreme and set it up as an Extender.. there is basically no other method if you are going to stick to Apple and not use ethernet connection.
If you are prepared to use ethernet to the dark zone of your house (or powerline adapters as ethernet substitute) you can use any wireless router you like.. even cheapest second hand ones as long as it still works well.. Here I recommend a wireless cable router Netgear C6300 because they cost $1 on eBay.
Another approach is to replace your AE.
Apple departed the router market in April last year.. so buy a new main router.. eg Asus high end model (RT-AC86U) or Synology RT2600AC which is very popular.. Either of them will have hugely better range than your existing AE and might well cover the house.
Using wireless extenders gives poor results and is actually going to halve your network speed.
Another approach is modern mesh systems if you cannot afford or rent the house and so cannot run ethernet.
Units like the Netgear Orbi work a lot better than older wireless router plus extender setups.