Can I wire an extension into a Party line phone?
From the 1940's till today Telcos went through 4 standardised system across the world.I am sure there were many other standards in various places... which makes things even more complicated.

DACS2 is the most recent standard that allow for multi call, caller ID and Digital data on a single pair of wire. They are usually terminated with filters at your socket.

DACS1 is what allot of people that were born in the 1980 will remember. FAX machines and 33.6 / 56k modems. There was no caller id support and having two calls on one line needed a separate pair.

1+1 WB900 about 1970-1980 is what I think you might have. It allows for simultaneous calls for two parties per pair but each party is terminated with a special filter. An easy way to identify this standard is by trying to find out if there is a battery at the master socket.

The best way to try and find out what you are working with it measuring 3 basic voltages on the line. on-hook, off-hook and ring. You need to be careful not to short the wires and do not touch them bare handed. You can never be careful enough with electricity. These voltages will help you determine if you can plug in a DECT phone or if you need to try and find some kind of other phone on ebay or something.

LTE coverage in your area is a perfect opportunity to use the up to 300mbit/s and install a voip gateway like the linksys SPA2102 or PAP2T models. You will then get a modern day DACS/DACS2 complaint signal and you can use as many DECT phones as you like. You can also redirect your landline number to a VoiP gateway or if you are in the USA Google offer some interesting things with Voice.(which is VoiP). Benefit of VoiP is that you can even have your Cell Phone (or cell phones) ring, while your home number rings and have an online mailbox that you can access from any device.

If in doubt just contact the Telco company and ask them about installing a separate phone. They might just do it or let you know how to do it - Or say. No its not possible because the system is antique and we cant get the phones any more.