Another Sustainable Growth Q

Why is the following statement true? A firm must issue additional stock to grow faster than it’s sustainable growth rate, given that the company maintains a constant ROE and capital structure. My thoughts: If a company issues additional stock then ROE would decrease, which would decrease the sustainable growth rate. This thought process is obviously overly simplistic. Please help.

I think that an assumption is made that a company would only issue more stock if it had investment opportunities with a return higher than their WACC. Then the ROE would actually increase causing growth to increase. Once they run out of these investment opportunities, the company’s growth rate declines to a more constant rate. I could be wrong, but it makes sense to me. Best, TheChad