Before we got our own reg set, we were advised by our LDS that it was ok to bring our own mouthpieces and ask the local dive op to install them on our rental sets, as a more hygienic option. We did this once and had no problem with that.
I think the OP wanted to buy a primary second stage plus hose, thinking that it would be a compromise between the mouthpiece and complete reg set, with primary second, safe second (octo), first stage, and gauges. Buying a complete reg set has its cons: it costs money to buy a complete set, it costs money to service PER STAGE, and a full set is heavier to carry in luggage. So I get where he’s coming from and his rationale for his question.
I think various posters above have made it clear to him that doing so is actually more trouble than it’s worth, with compatibility issues, most regs are sold with first and second stages, he might get pushback when trying to get the local shop to attach his primary second stage to their first stage, etc.
I don’t think OP’s intention was to go without an octo as some have suggested.