1) To extend a ring the best method I have found is use a quad grid plate (same size as double socket) and fit two grid sockets, it means you lose the switch, but you then have a socket to terminate both sides of ring so you can take a cable from each socket to extend the ring.
2) Should it prove not to be a ring, same plate can be made into a socket and fuse connection unit plus either switch or blank.
3) To extend a ring my first thing is plug in the loop impedance meter and record the readings, this means I don't have to open consumer unit after to test, as I now know what loop impedance I can expect, there are other methods. I will also consider if the readings show likely two much cable already.
4) With power isolated, and I mean isolated not simply turned off at the MCB, I can then remove socket and test, checking the line, neutral and earth are not connected assuming everything turned off or unplugged, and I have continuity between lines, neutrals, and earths showing connected in a ring, if a suspect home I will record and compare with readings at CU to ensure no fig of 8, but that is rare.
5) Add extra sockets.
6) Retest the loop impedance figures if a wire has come off when refitting the socket I will see a sharp rise in the loop impedance.
7) Make out the minor works certificate, not only does this show others I am satisfied with work, but acts a a check list so I don't miss doing any tests.
Since you likely don't have a loop impedance tester you need to modify method, either you take a chance that when you replaced last socket nothing popped out, or you test at the CU. However there is always power in the CU so that involves some danger, you need to assess the risk.
Although a multi meter has an ohms range, measuring 0.35 Ω is rather hit and miss, should have 250 mA flowing to measure, you will not get that with a multi-meter, same for the insulation tests, should use 500 volt, with 9 volt of a multi-meter again better than nothing but you may miss things. Although the EZ150 plug in tester has a loop test, it is not good enough to use the short cut method I use in testing still a ring.
However fitting a FCU and fused spur the increase allowed with the loop impedance means unlikely to exceed the limit, if not already RCD protected you can use a RCD FCU, so with the reduced ability to test, the fused spur is likely a much safer method to add more sockets.
Even in my own house I have not tested and inspected as much as I should, and found I have two independent faults on the final ring, I need to lift floor boards and get other access, so I have simply fitted a 20A MCB instead of the 32A MCB until I have assess to find the fault. How I got two independent faults I don't know, not seen rodents, but it has happened, so I need to fix it. Lucky I do have the meters, and whole house RCD protected.