Here is how this works: start with fluid conditions (including one design point, one head one flow), select pump, review the preliminary curve, buy pump, test pump with water, factor water test data to actual fluid conditions and see if it is within testing tolerances, ship pump, install pump.
I would disagree with the statement that "a pump" only has one BEP. There are a lot of physical variables (impeller diameter, impeller mix, underfile, surface condition of hydraulic passages, case and impeller) that can affect the BEP of "a pump" while it is being manufactured. Even after manufacturing is complete and the pump configuration is now a constant* there are changes that can shift the BEP (running speed, impeller lift, correction factors for viscosity.) Now, with all things remaining constant, yes there is only one BEP.
*Never safe to assume that all things remain constant, bearing and wear ring clearances will deteriorate and there will be reductions in efficiency because of this. If you want a pump to have more than one BEP, run it for 10 years and then test it again.
Ok, so the BEP is the theoretical efficiency limit and it would be difficult to spec a pump that would operate EXACTLY at that point
No, it would be difficult to spec a pump with BEP matching that point during the design phase. It would be impossible to spec a pump that
operates exactly at that point. Your system curve will not match the original design because everybody was conservative, so the pump will be oversized and run further left on the curve than anticipated.