was the only place where I responded with an FAA comparable reg where it clearly state the definition of solo flight contradicting the OP's comment.
I think the confusion comes from the fact that the FAA doesn't specify that the CPL flight has to be "solo" - merely pilot in command, or "performing the duties of PIC". For the PPL it does I believe but as the poster has a PPL this is irrelevant.
Actually the idea of a QXC flight is to ensure you are sufficiently competent to do a cross country flight and don't just do 250 hrs of circuits before the CPL test. If you are someone like IO540 who flew numerous trans-euro VFR flights on a PPL before doing the FAA CPL, any DPE would just look at his logbook and go "ok, that is fine". The FAA do stipulate some other requirements, which (I can't remember) but that one airport must be at least 150nm (??) from point of departure in a straight line.