Encouraged by the third hint I'll give a try
Phase I (solved by @Deusovi)
- bubonic plague
- ten plagues of egypt
- plague dogs
Phase II - Insert! Interpretation?
My leader was once, in short, an elementary British theatre.
An 'elementary' British theatre could be the London PALLADIUM.. (as suggested by @Stiv)
Palladium has the chemical element symbol "Pd"
From Omega Krypton Comment: Palladium used to be Pl in the early 19th century.
My fellows achieve, register, and branch.
log: a register is a log, a log can branch too
My tail is a Shetland fiddle.
So we have Pl-log-gue -> Plogue
And Quebecois use me to insert!
the french word "plogue" means "plug", to plug in means to insert
Phase 3: Solution - Stepping Stone!
Stepping stone = word ladder
Looking at the source code of the question we find "Look out for capitals."
Well, having two words ending with -gue we find the capital of the Czech Republic, Prague (thx to @JS1)
Phase 1: Plague
Phase 2: Plogue
Phase 3: Prague
So 3 -> 1 -> 2 is a word ladder
A stepping stone is needed to pass a river, gue in french is a small passage to cross a river.
Title - Nine is Three Tripled
Riddle 9 is divided into three parts