The schematic I am posting shows a difference between Merlin's and Pete's idea...
...The thing about Pete's idea is that the amount of bootstrapping gain might be able to be controlled by different sized resistors (470k or smaller) or by using a 500ka pot.
I don't recall ever seeing that Merlin circuit. But Pete's bootstrapping circuit deals with how the cathode follower is
biased. Since it is a cathode follower, the gain is less than one. You can't get any more gain by doing anything to a cathode follower.
Cathode followers or cathodyne phase splitters (inverters) are very similar in operation. They can be dc coupled to the previous stage (like the Marshall CF tonestack driver). This type requires no additional resistors for biasing the CF. Or they can be cap coupled from the previous stage (Pete's example, or 5E3 cathodyne PI). When you block the dc plate voltage from the previous stage with a coupling cap, you will have to set up the bias for the CF separately. You can do this with a
bootstrap resistor (Pete's example) or you can use a fixed bias voltage divider between B+ and ground to put a fixed positive voltage on the grid of the CF (the Paul C. mod is an example of this).
Bottom line though is that you cannot increase the gain of any style cathode follower. Gain will always be less than unity. Any additional gain boost will have to come from the gain stage that precedes the CF (or in a following gain stage).