> But the phrase after the semicolon is at the same level as the initial phrase
If you mean my sentence in the GP, here's how I think it parses:
A1 ; A2 . B
The two clauses in the first sentence, connected by the semicolon, are ~equal - but they are subparts of concept A. Concept B is separate and in a separate sentence. If I used no semicolon, I'd have three sentences and there would be no subparts, only A . B . C