I may have misunderstood, but I am reading this question differently. You seem to be asking if you can run the pump at a lower flow than rated. By stating that the head you wish to run seems to be an efficient operating point, I assume you mean you can achieve this head with the existing curve by operating at a lower flow. If the pump has a curve that is continuously rising to shut-off, the operating point at higher head will necessarily mean lower flow. This brings me back to your original question. The "rated" head of a pump is the head that the pump will produce at the "rated" flow. The rated flow is the flow which the purchaser specified as their flow requirement when they purchased the pump. The term "rated" is not usually used to define a fixed property of the pump. A centrifugal pump has a best-efficiency-point flow, a minimum stable continuous flow and an end-of-curve flow that are properties of the selected pump.
If I have interpreted the situation correctly, then you need to verify that the point where you want to operate is above the manufacturer's recommended minimum flow. And you have to have a control system that is capable or controlling the pump to that operating point. If, on the other hand, you want to achieve the higher head while still running at the rated flow, then BigInch has hit the nail on the head. You will need a larger impeller diameter or higher speed.
As Artisi noted, additional information would allow us to give you a more meaningful answer with fewer guesses and assumptions.
Johnny Pellin